SC 191 44b 


Raa 


“e 


after Wre Notes of 
Prof. William Ulan & GBV.C. See 


= 
Prof OUpplied Seal. 5. Wackingion & Lee om 
tember. Qu. Sos: ee S.. Eng. Club St. Louis, One. bngs Va aq. 


Lexington, Va. 
1894. 


Copyright 1894 
By David C. Humphreys. 


Transferred and printed by 


A Moen &Co. 


Lichimord, ra. 


eS kT 
lr a elit 


aye: fig 
ete) Ceykt 


“P. Q Rae’ 
Tanke Cid ee prerenkD Ce eubhies Beige 3 es 
student, Aas Me No RE ae MS primarily fou 
Mae We ue authors cLarser,and ce We Nope beak 
eee i cy ee ee eet to otidenk’s “efaewherr. 
2 BL ence ely er LIAL 2 mee of- tut hu ex - 
a a dd’ hed Be eth eon font et bs Pe ak 
She fate William OLaw IM.O. Prof. of Applied Math. 
ak Washington Se Low University , arubae menbly Prince of Ae 
Ml Domog Bo of, pubhished AW A873, Vater on Ravine 
Lied Me Sieer tea and Ravkines Civil ANNO Parts 
ka’ oo 
Lee Wriverityy , while Aeakmng & meena at the Virgie 
Milteary Snokileute , from 1865 Xo 18170; rey e coprows motes ow 
Cie soak of Bott these men, mig predseceos0r1>» AW 
as - swmne powell OR Formate Froave Calenkirr ou WPrewhere , 
wor Notes: the place from whi ak Ar RV AD WwW 
SS “i i — 
p at nae Ahak Ae motes tmurediate Gobowing ore 
§ 107 about what ir found Oat ane 164 , artrebe A587 of 
he Act , 
%o._ B'rrata both to the 19™* edition 1894 of Ahe text, and 
Ao APere Notes ree hack of ANre ook wp. 183-4. 


Lexington {Ha Hee. 41,1894. Cavil ( larf tee, 
A Sy Ta ~ 
She Y) 


| a 
4UNIVERSIT 


J 


~Oid x ® et Y 
r Pay St op 


~) 


y 
ricevids Cat Gnginecring . 
Peace 


C= conection im dg ae: CPama 


coh C8 400 Aliiansdct.. oe (A) 

C = 100 - f10,000- 4" eg (2) 

ae 5 7 (h-8( Rs €) = 40 flag Oe -F-p 
Cea Ei mean hy 


100+% ~ Zoo 


Os see ad va ie | amoll. 


@=cD:= mio moe A Bc 
a Po fe ey 


: e@= H = : : 

nr ae ¢ ant. the jot cA 5 Seat | on. 
Ri te ee nS Conde AC 
if ACB= Ga": ao 0 “6 


’ I 


SSB, ACB=30 , &= 60 , Seeded 


e’=2e2 
ACB = 150 » 45-60, nec ad =-2 = =-2¢2 


, 


pth . . Cor BDC = — Cor Ape. 
§26 AC*= Af*4+C8* 2 AS-CAD cos ANC 
4 Bc*= BA* +CA*, 2 BA-CA aos AACc 


BS-Ac* 
A &®- i3c* 


v 


BA-AD*+ BAs+CA* 24N-BA-CA oor ANZ 
AB-Bo*+ARCA* + 2AD-B9-CA cor ABC 


n 


Vie .. BS-Ae*+ AD: Ber = BS-AN*+ AN-BA*+(B4+AD) co 
A 


Cot= AC* Bd+ BctAD- (Ad- BH +AD-Bd7) 
ADd+ BD 


AC*-Bp +BC-AD 
ASB 


CD*= 


fae ee 


2 
. , Pe AR 4 Act- 2AGAe cor BAC $ 
eres Bet. AB%>4ACt*-14AAC cos BAC 


Be Ap-Ac:$c™= ABAC(Ab+ Ac’ — etc. ‘ F 
AL: Ac Ber= AS -Ae(AB*+AC*— ete.) 


AB AC -4c*-Ab-Ac. BC* = AB-AC(AG*4+ Act) —AB-Ac(AB*+AC*) .. 


At.Ac 
ve z= y 1 Le y & 
Be = 7/-At +Acr- =. (48 +AC BC ) me, a Rap ast (3) 


» = 
Ae. i 4 Ab-Ae 5 ee is (A$+ Ae)” Ab- Ae) 


2 i 
Ac = AbsAe _ Ah-Ac AnAc. AssAcr — e-A6)" 
ys 5 


Be =~ | Abts Ae* Sou 2elie CLEP (A BY; Aete wer) 32 (3 A) 
(AB+Ae@)*_ (AB-Ae)” 


Ch: CR: Ae: AS 
Ca: Ch:: Ba: Be 

Ck-Ca : Cb-Ck 1: Ac- Ba: AS: Be 
Ca-Ab-3¢ = Ch-Ae-Ba 


Gut Ae=ABt Be 


Be-ba-AZ zAB- abB-$6 + Beats $C 


= At: a Oe 6 
et Be -CaFzabB- $C (1) & (7A) 


Ae: Be:: AS: 4% 
be ae 3: 4k: a® 
AGx $e : BCxac!: Abx#h:anx bh 
AC. fe-aB = BC-ac- Ab 


i ee ee Ye 
he-a 1B -A@ = of. BC-AG + he BC-AL 


ak. pe. Ab 
ind at-AC- sesh (3) 


Aneo MM'N'N eh ape ant, #4. ; 


ALve poro8e 
= A + Bx + Cx? 
ean anna of OO0‘A‘A 


~ 


Area = {ay dx a [Ge Bxdx+Cidad 


aA 


Anea = 2Ad+ 2Bd*+% Cas. 
of the UnNve Qwer 
Pe eee 
y,=& =A+ Bd+ Cd” 
Ys = 4A +2Bd +4Cad*- 
pobewma thase fox AAAs C MOR 
have, A= bo 
B= -34.+44 -4, 


2A 
Cs 2%, - 44 +24, 
h a* 


Acasa 2hd- 38d th Gl Bt+% Od 8 da & Bot 
=ha[60-98+20-38 446-88, +4&), 


=td(b.+44 + 6) ‘ 


Anea AA'8'3 = $4 [6,+ wb, +B, ] 


ice hve Aotal mio. avwlt he 
= (4.+6,,+2(6,+8..--)+u(& + 4... 4.) 


Wismotwoal Seopae abe. 


‘Bias Ae Von oabes 
ha Adamkueal wat: Sanya on? 
Rake sk co mkroduneed Vere . 


ot to ma the 
wolume of om Se 
Wi ean Wek, freee ie ands ond 
anddte anrear, the Xreckrvonr 
hema para tlel 
he robS ro awppored to be 
cipal ch tar, ates aa ed, ae 


conrtanaree from awe ‘abe k Anka 


dy tha, othe: ; 
S acheia nots e divides 
amXe Negra. 3 Be oed xe : 
o Z 
Sor ECA g 
No = m (x+ £y 


ougen Ko the aperker, Fan = conrkont 


St uo uwaeds 


6 
Sor a ned. az 
Area -A = a (x+ $)’, 


Ahsan ett eater’ eblit ia 
A=EA+ZA, = E m(xt 6) 4Em (x+6) 
Collecting the coefficients 
A= D4 Bx +l 
Vibe = Adz = 
2d4+2 BA*+2Cd5, 


Siinmilonty Vax ol [4.4 46,+ 4,) 


ee ee | 


AGKI = Qrea to Re ec 


C= som 
F = Bae 


Az Qrea of AGK\ 

BC= a, Comrtont 

co: & , : 

Set the hraemg promt ha moved #rvar D 
a4 Len, ewordimakes sve Vow 


Anew ‘vs & eat 4 e* AO Ore ae 
oo SRE og 
. ead Ahe Ariana Le BCD s.ve e 


e*= abet tara? SORE ee ee 
A at 8* (40 ie ab feossi iS eee 


Simee ami measur rhe wet canes bap =7e'dO we Auppored @ 
enetant , ic chal Danian abi Canes oso he Anywor ed , 
constant during Aha tera movement”: Be ae ct 
ana le CBC = sige pap=dO@ 8 .. CE. add 
CH =”CC, ran DCC, = acosy dO ; 
buen athe component of Ae motion of the sow fe! 
the nstakion of the wheel Fo aamee At ahiSes wit the Sreehion * 
of AB ance Cp = hance’ @R*-04e Aha’ ‘dient akan wf he Attend 
Henn af .8 cs performed buy the w LF and us egual to bx 
ALe dirtanee prolhe§ Aha. Aupyores ths SEX poy at the 
point €, but bce rodent thar Lge werner poled ok ae 
aut F, aby vu Mtoe C, we em akion to whak — 
t. EF > 2 be Of 2D ohne? MIRALE actually. Wat he (On ¥ ‘ 
The nstenak #5 Aw” divdas aunty 100 pub wail the 
dOraXance CO= com $e eS Aaa to rreod 4 ann Ov 
Fas obharx. aw 70. gee J Voc, : 
Sf the pole B co outside the figure ka he ee ay ar 
9.3.4 tin Ae” antegrate Lelvseiv: the Anives =a amd o. 
G3 becomes, Ei avs b* Ab — abl wrt dd 


ab 


5. 
Sf the pole Pe Ta POL Qe area to ey mMeornwt 1028 be 


La 


Oe dias 
A= 8") 49 Bf crn dO. 


Re dN art hia obs buy the whol F 


Sk ol va honk conratonk ond =40°= 2, then Cosa =O Rone Hl 


As ar”; 
ae AA est adem Vas heniocb eee tebe be eke Wika otwoys be 
ade) to he reading of the wheel when be pole Ye imarde 


mre af pategeratlaes Jp. a 
Ne Phlamimer ver 3 
Annes the eort fas it do 

danned, 6 or T kumes Ye acm-— 


et 8, BDH Shera, af Borkon. and other, 
and Bee Kolber erent pee a. Warkenakon 9 € 


pecoll Me 2XMNRADLOWD of reveal 
se 


A vinwoboing te bakitude, 2 which 
A? , amg te Pak Lo We 


Deriqmaking the eajua tenet 
pan yas a, Whe Ciara. or wotar 
Aawnr- arco by Been Ahe eceent uct, 2 “2 enyvies>ed bx, 


. on rate F hg 


até 
ates ae mn. by, N= Grech) 


a (4- e*) 


he AmotiA of euwakure by , R= (i= etam BY 
be fatituse. 


6 
ee hength aes Peet of th Lokikude 


p46 ™, = var 15> 
§ 33 
17 R be R 
& note Me have 1m = 360x60 aoxte 
y Replaemng Se PAGE IO BIR 
% J TO ayn ~ 2 
= Tgoxbo (1-e)(1-e%san a 


pe a rhe Lark, Packor'c ae. & ale Baad 
Seal dig ce mony of sane J 


M = Beige (eV (1t Feral + Bet smnth + sie ) 


Sinree fer Dre waite 25s wey Amal (= 0.082271 , Clarke) i> fourth 


Ao eAL Cera Ee entickel ak Ga okiwon weet. Teailetiess 
Mie ao Tee a Ni eas nnn Be sorthken: 


4: inn, Dict Wadantle,. nas earl i EX, (1-e*) 


E a5 aos Zo (\- ejZ e* 


Let ™, ha xl. walue for om BP 4 t. Y. 45° 


m =O + Pail 


he ne eae 


= Plrinle£) Ar (£-2} 
Lek fel a25 Rieu 
m-m, = Pran(2b’tS) rand 
= P frn2b' can 5 + cor 20 sin) ward 


Ree PP eee ee, 4S ,ond evor2f'20 
“+ m-m, = Pian 5 aan = Pain 2d 


m= m, (1-2 ran2d) 


Wid | ar 2 3 2z 
— = % -00 2 (0.0822 
Z2™, 2x6076.36 boxigo (1 ees )x x ( os 1) 
MNumerote QVensmimator 
ii = 3.1415 9265 fog. O.49TI4 944 4218992 hou Le. O8 4-O735 
A= 20923583) “ 1.3206 413 10800 ” 4,033 4238 
6-e7)=0.99323 » 9.99] OH 96 -10 2 ei 0.301 0300 
3 O,4%771213 — 8, 4191273 
e*= 0.006763 7.8304604%-10 + 6 1224227 
+6 .1224227 aah se 
; 19802 = 2.29678 pe 
ee See ey 
ae TORRE Zoo mean by 


m = 6076.36 (1+ tains xbdtbagh cat) 


1.46 
3 3 


Tn the same way tat 


i 


Wewatiech Ahice’ value of am By anneg Me Pevrgth of 1" a 
9 as ee es ee a ee Ane ~~ 


6065.37 = 6075.87 a Aan 0" X 6075.E7 
4 


Se ee d=2-10° 3 At a fron 2, the Wea Acer P 


a0 os kbve ie bees of mM’ = Lemath ina Poet of Tow a are A 
erage ko SASSER Ee RO feat find its waloa ae tae 
N= Tein , this SGP FE eae 5 ee proce is one of 
Rit, ceickve ovat, be an, the ionie BB’. 

But m':im:NV:R 


ppt Bonds Yn, . 2 
am! ON. Pe (1-e mL) ek ~ OrAnm 


—_— aes 


* Wie R = re ee are ¢ 4—e* 
ree tie 
I om) and ™, Ly 3 ae aia iws sesh ia: A 45° 3 ae 


A Wee Aan AS 1- 0.003384 _ 04996616 
bs a at ee So. OY O00 CT GE = 1 0.993232 
, 3384 
Ot m= m (1+ Sa5737 ) = ™, (1 + 0) mean by 
So fond the general wolive for am’ we hase 
Pie ee “AT OL _er 20 )-% 
= F60 x60 = oe *hent's €) 
m! = £25 (14 fail +% Pitomy Fier e 3 
dropping AY 4efore chee Fig fron pete of @ ave Lasse. 
Oa, oe 
S : 10Fo 
m’ = O'+ Plsavirl ; ths} To, &* 
P = {5800 2 


AME found Pa uw 2 of mm we fred 
= mi - 2 ran 2d 

ik ™ = m, (1+ 5c 

mam (itdse — Ee an 28) 


Subsbibuting SS nichenty: Lag: ture 


1% Tae™~ 73 4 
am, 2X10800 X2% 601636 ~ 590,03 

/ ey Aan 25 
WM’= 6076.36(1+s50- an ) er os (2) 


_* Argnr wo mot ees) if we otiaeue. ARLE Penk, aN ordinarily 


8 
G, Ie Ae ren ees oF mm’ Ave wae ok 1 om i ene anne 
aek anoker Ae de O wa 2 vat ee woe Piss 


Hnoke Sears Coun foe ODer Live An. 24-0 8 2083 
BY rs FR. tcoo* + RK, arran™O ) 


pace KR, and R, ore the Vieak ee nreoktest pd Sk envarinre, 
fe uee tha ore Aubbtending A’ wanted ee. AMie: nadane ee ae 


p46 


m= oe 
which may Fe subrbababed fox an. Risto’ fquotion(3) when 
m>m’ 
She PS pe uakiony fotinutwea? ae . (4) (§) anid (6) acve Hae 
the figure queen SS AS SES | I 


a. waluas of ane de U.S, Coark Sunes , Report 1834 , 
Appenddx Ae.6, 


PrRoBLeEmM 2%. 
Sree 


nas FHS Anak = Arn $ ; developing by Sttaclaurrwns Treoremy 


: i. a" 5 
. ane oh ge ee 
ae \ a? A Eee ee es 
5 aoe “estes tiga 7? aosys re t are. 
Aamee Ah pr 1] ee £32 Ann & ; Se es ee Nice 
v| r H 4 
worXne am ALve obove Wwe qet ALve fe ge opproymnations 
; oe 3 5 
= = om X+74730™ penta wee A + eke ask (S4) 


S$, ele marrorro (45a) and (56) Moe Ankse Ao nema beak 
ee Stt (x - eg PH ies Xe...) where HL og anon dahia of re 


Aga tern , AM Ape Common catalase We = ASHZOLS 4% = O7T23E 24 


PROBLEM F*2 Fhn mounal Formnuboe for Ate crea of oO apherieak 
jrsoma te A” S24 (A¥ 8+C-2)7r* 

uhere~ A,B avd C frowe for a amit of mecoure one rug ange. 
q 14 Aen | ee S ae (A+340-2)40 sgh 


a (4+13+0-2)40 =X-= Sm ( te La 


Sa AED Seek Maaco eee (57) 


i) 


PROBLEM JV 124 werHop 


tt9 . 
833 Aw (A +3) = Amd eon 8B + toned urs 
Gasiuaned from Am (A-A) = Am ad eor/3 — lord Amp 
trigonometry 2 Aw? tT = 1-wmy 
2. eos” T = )+ cooy 
Cod y = Corel cor 3+ Avr d Anu 3 cos C .--- G1) 


Lurk 2 Amy = |- cory 
= ccd a sin = Am od Anns 3 cor & 
Iu ww ann 
= |- Cord orfAtAmr d Am — Am db Arr 3 ~Armir AA (3 09CL 
= | - corA+h) —(14 2 C) Ari drs 
=} = 0r(d48) - 2 cor? E Aawr & Ann 3 


= 2Awn™ S48 _ 2 eos? Aw 4 Am 


dividving By 2 Weer sy, adds Semana wd Rave 


pow LT = Am" 426 — Arm* D “ Annee Aw “18 + cox ai? . | 


‘ ; 4 A ‘ ‘ 
Awe ea awrrre. join? E = BP ec std Sie <t8 Aan” con” A+8 fe Neh 


= (sma STB co D+ cos 446 rai. D) (Sun U4 cas - 20-4 “HF Sen D) 
= Amn (448 ,p) rin(47@ - 0) 
ss Arn a [done on(2t? 4D) smn Gif 0); ys NBR) 


10 


Axe cart agimuth at 1% ie ncetia ee 
A= wert a re gn FS . 
p= fatitude 
bnctine Step hine Sab apes 
f= abtitide of Avil ae wtacrwesd 
“$Z 2 Renee 2 dirtanece = Fo-% 
w OS: 2D3’2288'= auecare of declmatuene 
telivecen ‘ical and herd obs. 
pe Phe We pote, Z the ent 
Aw the parallel Mercer Buy a Aon 
AMB a incon Sy A poroWel Xo te 
frovigon , and PZM the rneridion of rhe place. 
ie bhe Auamabe PZE wwe fase (ree Ree m4 Ea, 61) 
Coy PE = cor ZPeaez + 4rn ZP Anz cos PZZ 
or Ava(S-2 AS) = Ana @ am h = cop ake tae A 
Rae Avr (5 +445) = ang yer 4 - nrg ee cos A 


Ae di ference of sis giver , (sce RCL. pat bg, 13,44 % 24) 


2 car S rin ZAS = 2 tarp Pe Amn & (AtA') Ann -A? 


Pee pire Ad cows 5 
Sk ttt te nacennonns A> hake ADue nas: ie obrevnsakonee 
0160. Ae debounine AS. -SE cst fs ae 


Ann lL (Ave 40 eee 


Buk ee be 
Habe » Cos,S =awn E corel 


A= meg hk ACen DLO 

RSs wanton Kawire 

o = pnbttaXton. of Afve Bhintic = 23%" 
S = Lo ebiivee: packages paacOedad igesy 
hve wm: Le, 


Ok AL. ag ainr0x S = 90°- 23% = 66% 


Fa = = r*wmn fF wore 
Qt the equinox a fe da = dtjvs & phe No ae ate Rhee eee 
Arowels 360°, and toheang eee cetance Audweled Wa one fiaun 


= dt MIL Tee ° ; ” uw 
dk = ae = 002'276 or 147.6 
$ 


ae ad the equmnox ald = 141.6 K Aw 234. =. 59" 
Mie Foon ¢ 0 coushonbl ace: rec ices dd asaces. on Corl , 
Wn por, w thee auth ae a? ° ~y wrth omg Mbit cal 
A> mort quite tane , 79 


oe Patitude of place of obrere : 

: P = utude 0 eo (2) oknwon 
err” § = Se mation 3 AXIAL 

PE = polar Scrtaw ee = 4o°-5 

PZE=HB = A, = Ogirmuth at eboraation 
P isthe pote ,z genrith Hy hougon 


riamgle PZE ws ES at £ ro by Napiers Rube 
Am PE = cor. Comms. Pz Con. Compr. FZ¢ 
or cood = cos P trr A 


oe) 


2% Amn A, = ry 


ON 


4% 


fe ns Le 0 Aube, : 
fs ate Jee of tube; 


ma Aeconds = 206264.8 , 
hee 206264.8 ar y 


ot = 2062648 & ...--- (1) 


1.88 abs. lees D_ 
g 52 - | rs ZT = mean Otommeter of Ades Choke 
| / =. 79124. A4o = AITT8,000 ert . 
/ 
| / : Ap*= DeC(be+2r ) 
f / 2 
: / we pe= a maar by 
/ . bef 2 
° . diatanee’ 
| , ° =: aie ee ae 
y Corrsetion, for Cunvaliunre win fret i1,778,000 (2) 
Son AV, Sisto own ‘ ) 
‘ Coane ctiow nn fe. _(§280)* _ £2809 = 2 meanhy 
74124%X% $2389 79124 °° 3 
Cor. nin ft, =% (dcotance win mibes)® 2... (2) 


Sn 


HAC = H'Bb =40 ; 
BAB'= ABA’ mean 
CAB =ABDb 5 a= £p 


a= CAB = HAB’+CAH- BAB’ f. 
, 


A = ABD =y'BA'- HB + ABA 
/ 4+8_ 22 28 4.2 — HAB'+H'BA' _ 
/ Spe = FG = Bfea-p = Westen 


es y a+ A’ 
i “ea by 


| 
1 / Ss x= = £40" moor by 
| 


2 


p92 A ugyparing Abe ain Xo he art nrerkt, ak iia Sao Gee Bowing, 
957 hen thao oe aching 4” porte, =-3 nes pcky 
ee ibs: hinestiy of ADue OrrLs of Zand Srva.nie Ade Hreroune 
" Vode’ woth ALve devaky 19) salt eth 


dn =-qddz= webhtofaolt. HAS UXIK MS 


ft = C Pax; Ss 


Hak; z=o oind Se thre a id Rb Arena nre by i 
We . 4, =€ aes. igi ve 


tee 8s. Pont. =. - Ott 42 
S , Vo 3 Mc 
a Ht x0 Ae Bakes Se Aes of Ps a8 tonmmow Araphem , 


Ses ek st pon fA) 
Maautd’ Lave t Z 4, (hi = Pace hut of Ae CAA 44 at mpper 


Atakcon) | 

Reducing Ase LDS Sopa EOE ldseee p ho tal tt would 

Fave Been had the temperature of Ae mererry at the 
mot Jif. et Rive ARet at 7%é Lowers : , co if h ceient 

f aypanrcom for hepa wares: | being 0.900100! ; 

; H 


oo m Ad (1 +(S-€) 0.0001001) 
1 Oe a equation fox permanent as ses ore Abe 
Aemperature DPArres = fr. O(1+28) 
making O= o- . 13 fro DB, ond dividing Ade frst buy 
a Adcoind 


._ p re) : Fan: 5 
ys dies ) + De tts 


But mo matter za hak eae cur eae: Ge, 
r ~ fe i2 1+A0 


fc ee 
D, te: oes = * 3 ie = conrtank (ree wort p109¢). 


Ve 


ay Wir makiworw Dn A> Ane ees Oe WAere ak rkandord 
Eee abbas (32°F) ; g AY Ae foree f eis were Howoh. 
| Beh} WOLD akg bb with Abe PLabitviSe "Ran Revre conriderr - 
¢ constant ; Ra phiezhisk Re of the column of merewny at 
x Akan ard iiss woke waner ar D, he denrity art 
ptavidicvid. temperatrnre (32°F.) j coma uent by fou in? tomatoe. 
Khe lank tem an the ateee equakion- ars a tonrtant, 
presence wonies, for ASve Aame te 


ie kDe 


acd Re ss omer arn — 
Since > eoekkieient o Anpeos now for pommoanent : aA 
d= <i , and O= cL Ave Pa from AQre Fos none 
ae 
te = 9 (1+ EP) 


; y ; ib ais 


z= Se) yi Poa h(i +(9-4) 0 conical (s Ps pas ..-(B) 


) HSI 

anny aot ae Acareaby Aer mt he He or SorX rkokious 
a if cer bly AVUALSs aun app Dyin hie. Raina ta Set X denole 
Ale pele Aloe: Akchud Hae 3 16 wmto wo hehe ANee avkor ame 
wolva he in mbeinhies. 3 Sa wre tenporakure or the Rower 
Akokion , 75 ae AWA ‘ 


; z, =(I+ 3-32 KX 
If t' be the tempat the upper abation ligt toe ee . 
Adee AOWNWNLZ FOL Both , ES st 4th ye 
She aneonr of are ”» Ye Lert anyvrexmnokicoye Ade COM whee 


Z,t+Z,-22(1+ 2 +d 64) 


932 
p, pip 
z — {oq H Poa h— foe, (1 G-#)a.coeroor)t (1+ iat br) 
But .% (1+(F- +t) 0.000101) = — 000044(5-+) nearly 
2 aw G-k 21, Pali t0cv010p) = 00000434435 


S-t 210, tag (1 +0.001001) = 0.000 43 41 
“ §-r = 100, L (1+ 9.01001) =2004314 
1 for aren of Got herr we 400 po opyrormmotiow ir fore 


Foe 1S i | 
p22 DFS Fe 59 IN See. eye word ie) ae ee ee as baus a6 
857 


We eS en hak Deh, AAP 108 comrkoanr , we Con Aferefore 


51D, | 
determine itr woke bu musorurmd Bice ove eek re Dovel 


or theodobte the other quomkibios HATA OUR cans bl Be 
Mesaiscs Bartlet isha fay her avain by fobowed wan Bre 
Bekove denronrtrobion- quer On” tics tomratiank 60345.5! 
Bale Ranta fords at. Ko be 60360 ; Aubatitubima ee m re 


obove z= 60360 (fog H- fog h - aosco4u(S-)} (14 Sekt). A) 
Kankines fquation(2) 49 onby Bi cicinem ste ond the vabse of the 


conrtant Sine: ee he Deberminred £ co. akan yA id de ao a5 oumule 
at) tthan all the quomtitves ws E42) bs coonig Revo, eee 


conrtoant. 

oe When no loganit ares ane at Tee we Lanwe “aees AD. 
ee. of exparceim of wer = Spee 
ar 


fog ty = fog(i+ tG™ ), 
z 
q alee, iC ot ee 
en exade Ent © ase 


2 
Me Haid R' do vniot af GAR Adhata cee my mag buck atl but 
tLe furrt bern and comrsider Hah . £ 


oe F 


ee A 3 =29%t yok" a Nt = 0.4342945 fog 9.637 71843 - 
3 he H+ *L * .3010300 
x 60360 4.1807TH442 


Hoe’ sey = 524223 195635 
; = 52428 x - 64 : 
ez. 2 Wake (1 +1te = }-(3) maonrbes, 
Note Pita Bick = 30.00 m, ue Be 5 oe 
a fh! * 3000 ft. iboue Ata Leoek = 2675 ) Fes a a ae by 
then 4og a f: ot (3 of wat tem #9) 
524238 er x art ska) Wbnte ast ee Ahal mea becking Ma Adana 
Mom: nn Ake bee boprnenk ar 24> Aone ran aa wakion (3) gues 
an *M10ncowr neat Au 160 fe. abou. 


oe 


nice . he Safle kaon ange Oe 9 


Sak oe 


oe tre ars ae 
thous a eo 


pubbeudad ‘C on one 100 Ft, Loney 


AOE = Deqree of et 
CAD =D Deflection Angle 


ae [\° eunve , 27% = 360x100 = 36000 Te 5729.6 Rt. 
_ 360 . Seowe ; _ £729.6 
er. oe Ys ~ LAY = =F x 100 = 22556 i Te z 
soto Mey 2, BSP 4 100; Aeees & ie CEES 
‘ = $729.6 = Deane 0 cuvakure =Awii- 


i 
" 
312 


. . oe 
C szr amid =e Am iv 


Developing bas PSS PIES 5 (ecu 


3 5 
c-wr pS & — tke. 
(% 77307) + Spee E EF) Try ) 
3 


ao- TE MAA 


Cz a(i~ #5.) meor ty yer (5) 


Bb = DK-DH = (pF-+FH)(DF-FH) = DF > FH* ) 
éc* =8H-EK =(EF+FH)(EF-FH) = EF*- FH 
Bo’-£C* = bF*-€F* =(pF+eF)(pF-eF) 
= be{or-(D&-DF)} = ve(20F pe)». 


% 
tr =ve-pr ape {OF 4 Borate} 
2 ZOE 


uss, See Ga ee eee -----(9) 


(over ) 


FH 


tT 


Bp* = pF*-FH* 


2 2 
-. BO +EC 
€c* = EF*-F 4 


= DF +EF*_2FH* |: 


aPu= Deer — (BD +EC") sc... (A) 


2,2 
2ru*=(DE 4 BD'-£c ea Bors £6") Sigo% se) 


2ZPDE 


DE*, Bp*.¢¢*, (ppt ec*)- 
af ee eS - 
2 4 2 ps 4 de oe 


2 2DE 


— (Bv*+EC) 


a. aqmatwon (A) obove, AVE Rabe, 


Bk = 


DH = 


pe*_ gp*-£C* | (pp*- £c*)* 
2 


2. 2 4 2 
ey = ViLOF + £F°_ Bo ~<cr} (10) 
VL ho. Ee eee pee 
‘ 4 ( 
oe — eae Ec*= EH-EK = (EH +EK)* (EH -EK)* M) 


RG=2 547 tc... AZ) 


Dh = Cams a’ 


TE = Camizd 


pe =oT+Te = c('+e) _ 


ye oe 
ceé-AD 
1rT 


DET= 


ce (Ac +¢D) 


CE* 
Gare -- 22s. Se 
BC = Cami = ett! gt 
LT Ewen cg 
pitiless 3 A) 


109° 


410 
8 63 


ver in 3B = j—-7 141 -vew. aw B 
9 
O44. a ec 4 4 — Verdin B --=- {1a 


YT: ABIL: BE ‘AE 


v= ABBE .__-...---.(199) 


Aé* =AB*-BS* = AB ec" 


2A =27 2 6c* 
dl AB % 


Grom (198) es ae Sy ex Be inchs Po oS (419) 
2_ BC 
27VAB = 
warp B= AB OCS Geel a Oe 
AB 
ED= TwmAm BB .: HK = La T wersm B___._-_- (21) 


By pbiminlieon st i bees fans Mak We tidal wave follows Dore by, 
Abe Cre. * = wax. 


19 


Mm = 206264.3" 


Set 1 Ma te eS 
| = Tne ad = a aeon by 
+ ark + fg arh wear by 
4 k “ es vark 
| / ant 
ey, 3 +t Es Tr 
| Re OF a Oe = Vio 
. - 2. i ag Se ’ 
x aye = Yo 2LO6LbL48 = = S74 fh. vin feek. (A) 
126 
t. GE=ED =De-= CO 
$34 m:4:: TA:AP [:0E:EP vb es OD 
nu¢tiitl<«) PE+EBP: EPs: DP: EP #5 
| Wayeek 2) PSE eo eee 
| 
| 
2] i 
384 yer BA -=— DS 
| 
| SC = AD. = bP 
: VW Ares OPPs -BA- SAD aes. Pe Digg eee (A ) 
| M~-j: i EA-AD: AN | 
m £A~ Ad 
| m+l ili: EA+AD: ig ~— £A+AD 
: €A = 100+m mind ADy 106-11 
Mot (100 +m)~(100~m) _ 2m i mM-1 - 
| n+i (100+mM)+(Joo-mM) ~ Doo aati Sela --.-G) 
| 
| 
eal fale. a ‘ ALLAN ate ave ee to es dann 


400, tel, free. 


20 


A 3 j= €4 °C C-D=8-d 
T-128 B l= 6+0).*° te weed 
§86.A Ana 8: Ania (D+): 7 ‘f Sic chnnaal (Ams tia 


- Arn B= TAne{Dea) iad. haiks oes 


Amad= Aw \ 


Annee x and Pont wor A : “ 
Am B= Ams 


. . * “ Yr ; eee 
| ae -. Ames ~Awmd = (B-d)Am = ae ee) 
/ = eaeae 
CC} yt ey 20s be 2. yeetlrs) ” et} : 
x } pa Amy yw a Minas Bee = 2062 G4 8 


N, 


D 


we Raia ACB =Ane— 20626y:8 Cpf APC _ rm SpE } .. 2s 


SS BONS 5 ir umiverrally applicable A being afuows the farok 
cor hy rhe naught 0 aan an alieaiga scanned aaa 
and xo ofan fess Afar (b+) 


p.129 Supposing ie arrchkraction te on phoacre ak one 
86 RB. AMA kee eh ckive g arearkns Sata 
8 sleet 
oe ag 8 ee eae 
Ana(Z-Oz) 


wt Ama Ze C(Amz cos Az — conz Am Az) 
Buk. ton Beat. caidas ue maonr by 


» Awaz = Camz ~ C dz eosz 


 Dbex Sto) 
Ahuk(I~¢) Las Seen found buy obisercnaicveis ko be 58". «. Arete 58’*tane 
a complete anuerstia ation of Wie fans ia a ieaindeae rotkwun 
enkire Aakisfackion”. It depends mow De Poy dirtonee bh basoeicae 
ker, and the attashed and SebacheS tRennometers. 
Bee Doo bet lds Poilieak Oitromomu p.153 ) ale CLakvencnsenle 


Mosediatioie of bhe Wan binaton Obrewatory , 1845. 


\ 
\\ Sums CANT RE 
‘ 


fix 
fr. 129 ee fr. 130 
ie < 8 86 C. \ 
& 86 C, te Ms Se a ; 
Bh tine a MerHoo : \ 
lone’ Z the -— fantasia 
ms sf ‘. f ne { beet ima) y, 
ID MerHoo ~>~_ eae | fiiqy i 00:08 
- +o0 
HABIZON | + ie Tt DA 
4uk 00= 04 &rAop = 0A coo K 
me ia = tT ctor 4 


N.8. Sm wack of iat 
‘R” Pisces Me plane 

of XY conkarns bbe 
* se caniuawle SE nse 


B 
of fhe 
Ae . 
hie ovee R“= R ar ean wn ig. 3 

of tbe 


> 


Case IV. 


Deir ws B 


v ‘ADe Ee ch the Sieven. sain owe tee 
_ Sieclageyge adie! 


o ee ame ae ¢ gar sirens a Rha he 
Rie 4 nbc. hea 2d) Ae R” Le te 
STE Sa ee 


uokion» (9and (13) OW Ae ST fom for ADe tor. 
Rhetiseer tivo Lines vn ANOLE . 


z 


J FIG, 2 : FIiG.2 


¢ CASE Y 


a7 


DISTANCE OM = NioWeNr 
MA = COMPONENT WHOSE AXIS 1S PERPENDIGUZAR To R 
AQ = ” ” ” 7 PARALLEL 


22 


« 
aes 


We - Ws W 2 GG: GG,: G,G, 
We: We: Ws GG,: GG,: GG, 


GG, :GG,:: GG,: G4, ...---(A) 
GG, GG,: G,4,:G.G, -. 


GGya Ge, Ms... ts 
Pisin Me proportion (A) we Ale ALoak GoG, we porathel Xo G,G,. 


G. 
P.156 a tional. 


OA=AB Adv=40C and Ap ioe 
$105 Cp = a + Che trioma fer 0G4C md AGD me 
Armor and 
Bn=7 06 


Sh. Ante AGS eee 
al Xo BH and HD, 


EG,=-$8&6 5 EG, =5E0. 
“lp G4, <2 parallel to BD; make DK = BH 
ABC: ACD :} BH: Hb :! DK 


pronoriione 


: BK’ 33GG,: GG, ; 


dit Sayre 015 heiees > ronr G Xo AB, 
% Samce nwa. ACB and BCE ore 
a proportional Xo a, base. ie 4 cai 
£.,(8+)) = if-B +244 
“ f « a B+426 
‘oe axe 
fut x, : fs: Op X= 2, 20 
On £ g+2b +26 Ob  2.$ ™ 
ee a °F B+ Xe = r(\-4 B-*) 
We w a+b f eracy tae OD Am DOB = s6w.00 B+6 a 


fe) 


So 
p.157 a, aan, 


ond (22 etki) 


23 


A 
8 jos Mii kee plane of BS tA HQure ox O 
ag 3 Fe OF=% ,0D=%;0G=x% 3; Qua OAB =A; Area OCE=A, 
Rite / : 2 
if, LF aaa) S FS Zz z . % 
ee Dp. ef ih A, A, x x oe A,= A, =. 
H 3 1 
i Z(Ayw A 2 =a al ee x2 
LEI. ee ieee . sO) 
-~A a & 7 
y. a bod 1 se A, (1 3) A, (4 =¥r) 
ee 2 yy? 1 
z yi 
Oren ACER = A, - A, An tae 
ee 


AH = OH eot. OAB 


A 


1 


4 


Onean ACEB = 


? 


A® = AH — BH 


BH = OH et OBH =-0OH cot OBA 
OH (eot OAB + cot OBA) 


4 OH* (cot OAR +eot OFA) 


7 AB- OH = 
Auk OH= % Ann OFB 
2 “42 Re L 
& Ann OFB (cot on8 + est OBA) oe % 
4 


“OFB (Cot 0AB + cot 8A) 


ew 


x L 
Vessas a san 


A ~ Segue 


Here 


0% AR: origen and aid AO apie 


piers equations Bie een: Hae 


ie % 
} DES A lect ian "3 jam 
ene Am el i 
: Be cam i een 
ae frame denn Pega 
: [Pay dy Anno be" J’ 4 bx 
BS ainkie, a Ki 
ae a _ SFE oe Sie 
| 5G i ok SG 7 Rs 
| tC re x 
\ Lpy ky : 
for . = fps = = Vopr, = % 
Ra X* oly 2°3 4 
Ma wo fy dy Amin = wrimd vip [url = 12 Ania Sipe 2 ; buk Vip = b ’ 
¥ 
W= Faw % Y, Aow 


Z4. 


/ 


W = we Rue of porablete OABC = c7 Ky Am od 
N= weigh 4 
W"'=2 Wee hi of S Mtn CAGE S10 4 seed 
;: U ne a ; ry is 
W=zW = ¥ » Spomdail OBC = aw ky, Ann ol 


k om 
iT] 
bs rl- 
x = 
—r SY 
sc eteeitis 
= 
! 
a 


3104 Ulenrentary DALOL =tar-do 
Cae ts moment = Tdr-tor9 dO 
rm a +9 

¢ ee . Be ade qe gor 9 9 
ee LaMar. gore ig 
ekg fk dr a) 
AY k vs. ° ~O 
3 ; 
%, ~2L AMO Aun 9 
YY. = re oa s+ 
Y < Y to+2 re) 3 0 
W =w +0 


p-'58 Carentan Half Segment 
$104 A Sector . W= w OAC = w +r” 0 


——,, ] 
\ j [irae feore AO <9 
Te aR 2 i 2p eae 
¥ fr der [rds tty Sy 
Ra we ve sas Jirtder (race 0 de 2 gp 12028 2 2. paw 8 
dacs ; rig = Cl] = 4 =s4 
- > @ ¢ ra 3 9 3 ae 
oe Bt : X [ir de {re i) 
° re) 


6~ ° , ‘ 1° ; 7 . 
asamale ; W=wat Amn 0 wr 5 Y= Fr cor iy =Z7T Am 9 


’ “wu ” 1 ‘ 
_ We- WY 179, ty And — ta nm9wr8- Zr cor 


bs = Be = zr amd 
ee 770 ~y 1 Aan 8 eo 8 ~ 3 O-AammO 8 
: @ 
Te wig see 2. 21Ams Ao at 4 : 
W _ W. aT 0.317 2 —iT Am 8004 0.57 Am O 
= ° on 3 
4.2 a = 2 8 <= 
W 77 (9 - Am9 cor 9) 


= ty hArant $ — Awm*8 oor 8 
4 = 3 S. Aa ae 


a 


25 


| ed a P ADX =ABXD-ABKN = 
405 Tam O(1-cor9)r - T*(@-Arw 8 cor 9) # 
Yr ees 6 - Aun 9 s908 - 8 \ 
2 2 
WES mare Shain, 0. 2 CE Oe 5 
° as 
iy OPN: apenas 9 


) = Tr (1-cos O)r {1 eo28 + TU-w028) } a 
2 ; yams rosa 2 
77 (8-AmnG0r6) 2+ Aw 


. z 0. Am O evr 8 
- . ’ 
= Mlomr0- Ani8 9) (cvs © aoa ee T* Ania’ 8 = T4470 - T Amr: 

: 3 

xr Yan o- Amr ®@ cor 6 8) eS a Aav0 
2 ap: * 6 
r Ann 8 

% 25 


3 LAim O-~ pn 8 8-8 


_ 70-200 9 23) 4 AWD - rain*B 009 8 
ie 3 O- Ams ws 9 
3 
= 7 Arn 9 (1- cw 0) = 24 amet 2¢ 


- Ain *8 cos ©) 
ety a. 2 Arno cor © Pe A ) 


. _ VT Stun? ~2 20n'9 209 O- ran? 9 
¢ 3 2ZAMO-~ Aw 900s 8 - O 


me Sector of Ri 


x 


es ACHE = OAC-OLF. 
27r0.7r 
ae vor~en OAC = z 


J 4 
cs OEF = ae 


- 


“ ACFE=T O- +6 = 


O(r-r") 

7 x" = ALseirida 2 Cc of G. op OAC = ay Ava S 
a Y % = = " y » OE8F ~ 2,’ Aanb 
° 3 i) 
x O(r*-¥") = 70.4 5 oe don 8 


pt Sq -tan0 
eo ee 


¥,- O(r=1'*) Pee 2 FAnn® ¢ 


XU Spuettitlon WeSqe 


waytat” a Xdy =- *, dix 
Se XI awe Lave , = frig de 
Song det 

- vs preg = feu dy 
| ah fytdy FJ frvg dy , 


=Tamd , x= T orf , ay =-1 Arm PAP 
+> i Fo L wr? A@ 
oo Las =| mat 
+2 
Ye br! = (ae g ws Ag 


(ree text p40 Eq tl] 5 | | 
1 Aw @ a “teat 7 2¢ ie Corp = (beats nde we 


z 


Aung can’? 2) a = “¥ z 
p 
m z 
oo ers - [do —jooe ag-4do)} 
un 


y r] e vid i . hy 
=f [+E - Gomi +i rm I ( a) 


23. 30r = 2.297 sanz, 
oS ee 32 qZ, 


Mo = ar ? ro fe] ) 2,- iy, = i716 
S ' 
W = wr fay dy Za tt el ete 2 
4, “we Zz 1 4 ye 2 Pe. 
= noe ag ee = - 0 oh Ca RY Dm ea 


£159 
3105 


ibe 


.: 


27 
XVI Deenasdon Folge Geis Serwenenlor Wedge. 


? ; Way 
We asc fr oO, a, to wen, 


U “sey : ’ 
=z=Wy-Wx end Anice Zo y 
° ° ) 4 F 


XVIL Complete arte coe Vay So Tn 
tae Ate, ania of moments Merouagh ro) 
cerkar Xo ke ylame OX? . 


Area ABAC =A 


local Dee 


oo. Aen ff 3 pus Pek ko AMe 
2 Phy AAIe Qe sé 
es Ms AG, 
raat Wali. = AY, de ten 8 
moment = A 5, dt win © % 
2% _fonshes e ak -ih 
Pe tm OFS cb 3h 
Want, anne [Pp = we A ano = bwAh rim, 


XVI ETO a Come on Raynes . 


SEE FIGURE Saki Abc abeve® hekeithk oeetiseen fh Ceca 
ABOVE R' a8 noe howe ed 
= eee 
= wT fpr fe") 5 prgt 
peel | Mees EE 
W = ws A in 8x = Las Ah 1-5) am 9 


28 
‘ms BRerccold Shell. 


Vil eskincalred oma 0 XO 860 wh 


$105 pe = —& fo ‘alk perpendi es Aaa Ox, settee 
; CS --ss80-5 I ry Ne 


.160 


radar = erme. 


Arn of monrents = rod, 


Tg! a \ 
ta \ Ek. Vol. = ede. 2m O6de-.dv 
Ys ‘ mx. - yy EL. mem, = e° de. Aw @ car 9 AOdy 
SECTION BY PLANE XY 4" 
N.8. 7WE AX/S Z 1S PERP. TO PLANE OF THE PAPER peeks de fu Owr8 df yay 
ms *d0 [ioe 6 AO far 
, _ irr’ ), 1 (Amp - sina) 27 23.7 =. cont = cone 
L (ray 5, (- tor 3 +cord) 27 4 y.F 2(tar8~ carr) 
mm ae cas + Covad 
. sca ae ie 2 
27 
Wa w | p*de Foaae 9A6 | dy = Ar" #) (- tors + card) 


CL. Yok. = eo de-r»mep dg- 49 
EL. WMlaxia sm Z0Y) = e*dp.rmgewrog dg.do 
” or XOZ)= Cee con 8 AO 


_ Sede i qgqeuragd@ [ee 


= A rt-x* 
Ke gs riy? 


’ +8 | 
Jee [pate sis Jgnes bas (et ° dep re 12328) g =3(8-0)-(eon 


Pig { : d mies PF 
[ede [Fang dg f okt 
qlr’- x") £ T-(Ama 8, + Am8,) ye au tam 


ee + 9 +4) (~coo¥ + ev 0) (8, +9) GF? 6 
W = 23 w(T3-7T 3) 


tN 

J 7 ‘\ 4 
AG \ 
ao \ 
ge : 


pert, Se Fee gh ees ee 
\ 


™N 
¥ 


29 


3f Abe AML WAMNE Ow ABCD te mmukotmw 
ie porollel soa RTL Ee 
where evide =a tomatank. 

If Une it A> manrkorm panied 

ws Le LOK with flard MBPAAAMME , 
napnrerenred bu Re finder 

ABC bD-A'B"C 1D” - ALe prerrune an plomes 
wn , ZX premure 
Vorrer a ba Bas Ae oded por 
Aion = or 


YB Se 
ee aa peas gon from thee 


ot se mr. Arg, he 
= = HORTZON TAL ae Oe Ariana te OCE =w Aw 
Pp 


oF 


In the 
eager 


AA? Am fo] 
as 
p 2 
62.4 Ss 62-4 Yoon ?_(B) 


(9) 


wotdite Ahe werkizal onda= 


sphonve of XY yor ABCO. 


same ye 
em : : 

iomgle OC& or OCB’ and qo ching 

pimee ee YX 0 AA gues ey 


On AL. eevrbre of AAA: dis ko 
Sg ; ees 4 


fag oe 
m rt a 20272 “~ samatonk , use Pskek 
%, = 1% 8 yo 


L 


3 


if 
L 


ly ; - 


L 
Mie dintance of 6 from OY Le 
%, + Ste! eee 


dhe Mean pereure qr. 29, fk. ta Flatt) sent = 04) 
2 
BE, ace ARE nheaw oicseule of tee Krapregoud ABFE X20 
So. 4 (42%) EP Pre 62.4(%)- Xam oy 


2 


B da bnaMion, or megrnotw AD. Shs Banca Ade 
£6, , ond %) Lorie so 


3 
Ke = Hen Xe | 
3 -% 


Hace he ford rap haeaDhy 4 fund Le Cof of ALe 
wel J Zee ree 
Arapegoid DCKL nd meager nets Ae AA ANonwar Mm re figure : 


INTERNAL STRESS of Sotips.. 


[..166 Se a rt nr Canon of he Ambyeck AL Arnis Ay /te- 
$108 ferred a) ADe Onn. Htech. and te Ov paneer hook buy Prof. 


ae Legian. a PAIR OF Conuugate Stresses. [9.101] 
y Sek Yor represent, me Avctiow a gwen 
gy) 8 Aare a body, ans Lak Rhee. atsess. ene 
¥ = ee ¥ Afrak Lorne Be wy De directiow of XOX. 
2 © Consider the covditiow of a wirmnokie 
¥ porkiom of Afe boda Aeprerented aw Aackvo 


—,." 


4 


“} 


31 


le Tm bp Sar ae oxces enerbed Any Ahe Lit Paik Pe) AL 
3 Badu ts ALre faces AB oa be o a wining thea er 


he Be Mave faces Ad and 


a Vebiee or. 
aes orrapt ‘ey ae Cannot be a aT Khreir 


ho: the. Dane VOY -% 


IL TANGENTIAL anoNoRMAL STRESS. 


(See Anprlied Mechanics, by Jas Ll, Cottertle § 182) 


eo comping a toad P. On’ a transverse 


Arction 0 Oo sa eetattie rknere a produces 
Al Now) ie Doe tale iow otliale one 
ft 1 Veo RISEN siin tae nw p. rw 


on e es. Ye an» of thee har’, ono Por 2, Pape Ss 
SiGe = he ae lags ‘eetlag 1598 Nero ane 
: perpend amd aa os 
EE etlion. Be ndwnal component Peo» O > 
produce Oa dineek Arparation atk AN arekion y Sele 


| es a Y wet ners Se Seg Pty: Ps PRS ee, Xo OW Pe ee 


ete Heckion-, Suk of aN cei, 


Fall: A: Oren of pedinaasanae Axeckiow 2 Lae AArecd= Qrien of 
a wae tke wtensity ye) Ae ae ASS Akneos 


P 2 
T= qe O =peor'd , where peek, 


Bie other Component Foam ® prodarees os Aacgentecal oe eg 


1% ~ Anaad = Wary es 


32 


7.167 of a Aewsile Loin a : 

$108 Ones rage AO eb. offers gr0eat Sees to Sireck 

Reg irs nee « Briere acs pass 
7 mate 2, OW, 2 Aame v 


: “04 wole “of which io TF, ccers on another plane 
atoning rhe othe — settee. onabe of 45" We rometimer 
fond frackure Ao rigaid atror tiwo - ob fide planes ; A” omehimes 

> ee pete Ya Wane cor9 we 0 Anke 90+9, fk dar rhe 
Aawme value Metin er sie of tiie henge 
Atrerres on ° planes ye) 


” 


eres of Alreas ar. 
he Acew 
TANGENTIAL STRESS EQUIVALENT TO A PAIR OF EQUAL AND OPPO- 
site NoRMAL STRESSES. Dirtorbina Strer . 
Jin ADre eramaptbe AL Caise: jek tonsa MIE 
tae Pe e ho shearing Ode weed akrerr ; bark 
{A BI Necie’ wind) wiviai’ ebeinvion tate ee : 
| y Ov shearing Aknrers. Let ABcb be wa : 
|r narFamgulow shoe of Nizekrvess t. Over thaz 

t | A ater BC aud AD aupyrore a Aang ent 
flo____cl « uptohe Ce sales onstng Ay « Col brnag 
: , Aprancbd a. -the fs) Ae Yasder of the : 
ploe, Whe total Smowit of the rorngewks 

Uners om waek oe iv 
P = fy bt. 


JF wrk Lee Hviminag A of tLe 
Aunfacer AB’ and oC of ‘4 % F 
ADE . 


on 2 of Abere y 
Q= py-aet. 
P mut he ho couphe Q. 
en | 
ot q,- bt =p.at.4 


on y= te ; 
Biak i» Ahe inbemsichiy Spa! eisai Eis Wakune ow AB 


ar ow AD, 


é 33 


5 5 Ahere fore Panne ect along one qlane aonb 


2S See Be aces Lie Aree dokeous Akntars of Sa 
:* antornitng re Oe Hct akag ong lea . oop oO pain a, akndae 
er ena be weal Ak-rerts , constitute a Re 

Dickinbinng Shners 


161 


NF pee clot naib tinctcria aniche shore: Seiwa 
\ <3 ! 7 H 
ae ey : is Oe Xo €e A Qsane » oe. ee 
Pc Rat Ba AP ae pai, _ “ep es ae A» ts erent Are 
Gee fou wi tt vw perf oe. PY Spe ce 
4 Ax it fodier, 1” pe aro yok cone & 4 th. 
: Xe it shearing o1ce em qvroduces VB oa 
i FI Ang 
pik a “_ _X .P fe Aquecive ABCHD aceanes gS res nM ~ 
a Peek : AB'C'D, the tp dirtortion 
I On : , 
= 3 ba bas RT x ue. ae 
ee & ie ee Sy wW 4 eee, lS 
P P zd, jleag aorrte 


oes — Ys la of an 


Licey, & Ae myer sd Connon Cw, 


C eo . cobbled ua: of Anawiwe wre elardionty bark 

i a oie A> wie ee who Tg AL ow 3 &, ous per wrong hh- 
now Geiss ers he ra a ar 10 ey 10% a eg 

| Awe Now Fipats coax: ALe Akrerr ow the ormgret Aeckrow 
RE Fe ne Ane gent ol “component but 
Ahk Ae Avo Aunfaces Bee Le ae Xo pe PE Sea force 
jee a “oR 

J 4ue aioide 8 once’ AO ig OAL OVE el. ot Me eke ais 
Wahikes AVE Pos 


aa 
reg vai ks Rea ee = ae 


“aes ored AD Compressive “o te wat Re Ge ween oe aw 
ce opemeers being ope ond = th 


TTT ae a appears AL oA a afaavinegy AXtrers neces = 
= = aoniby tio ey Aasile Peer: git anes aa wate AXnerre+ 


<= Ee ow wlaner at night ler Ao aack other ond 
ak i eiSiat det mmabect oft 6*td Ble farce, of 
ASve A feanrinng poege — 


iy & > 
y “> 


oT ey ws ws ¢ a " 
&2vV¥ Métvi di 3 


\ ty 
‘a 


nt 


3s Ne AWKAD of Lf. Tews 


Athpivbins: ibaa to Oa Care of thearivig. 52 
2 


3h 


To R SION Cstterélts Arp. Mee qr. 358 , §/a3) . 


io 


Jot-revesinde aeouasaee £ a A of 2 cae irnaicctdya andes Le, 
1 qoin of 29 tre sik Seehis 
SS ee oS Pe of asta. re fess of Ae counter notaciail 


Wien: sw e-teoieihie Ale ate foree es pins: enw 


EDIE NY be 
ok one Ane, ocked prow 
by Owe vic foune tomgewkiol 
At n294 of avkewsity 4: 


a 
__ = 2, 


dA = diameter 5 idee ; 
+... titd s Atl iokne area of kube (arynox) 
qntd = ketal Adieu force , 
gata xhAda=h qutd® = hokad hain ¥ moment. : 
fixed awd, CE Avcansdi teh €. ngttindas kane bee om amiforne 


4 « Ae. ~ j ~ 
Aa’ $i, hee /> 1244 “of enritn 4 . 7 


Let AW? Mmm apisiet sae a wo 


of AG» Abe, ies A ats Baer OV Aarne Pee | Longitudinal 
nacteend Sa balonte Tie ake Vee Yue _bnarsaabeana aaee ihiaae 
An eatbes ame ackiow aw ean Atkn2r? vow ea Xs vhw ae eee 
aider, ro rhe trong the of We Abe Ae resist. Morrow. Pare Pe 
Or fectnable Senkee <a if AX ASCE LHe. ake a Udimol rtripe 
ar Ak wt Arawrwenrelu. But a we a ayauck pkitr odin 
ona te of A5° (SS an fa), mo muoateriok feima removed, Ahe strength, 
awoukd 5 Wii warred » Waa wad buses ey a C vi | 
Kain rides rrersed Aogether. Onother sk ot ara het sonnailen Ae 
BS agen (s's’ an fig.) ope Oe te Co- ersrow "om bove Akcdisonn 
aching perpendicular Ao Qe Sividing Arrfoces rratld Arponorte 


A 


CHANGE fe) FoRM. She te ene obeve Pegs roe eee ie 
ato o wmburne Lb taht age AD on Ahe Aunfoce of tee 
Aube poor bbe t Ad Ubu odin ware be he Awdintan ips sie 


thé ihelche ia? anes haz ALe oe ok dirntortiow o i 
the “Shae fet Bb Chat onal rica 


| 


ee) Bete ae aoe 


161 
103 


SS 
wb xo ttank 20 Fe tiem Rs hieult iek aie 
The effect of Weas Rae acbativel, Xo oo at oy 
Dre Awisked Herorcarbe ow omole DOD’ = + Amryrore , colhS tLe 


anate of see a 
LER oo ee Lt ppd lo, 


tii. PS 558 IWAMQDAIMAHW Va + 
a Az AY Armkt: anote LE 
e, a ee Pail wees o- + , ia eS 
TORSION OF A SHAFT [Cotcerité 518% fe. 360). 
OF comeenrtue tikes ; om AL awe of OGY sh gee Av auf ficcrenk 
gence Ar applied Pa a ak Menorah ¥ AAW mabe ey 
Pe Ee a eS 
Caz UT, Cy, = m ; 
yao ns rrd> Ake ankers bey of AL o1ee Anest Nae Ave oport ional 
thro ss Ae Aone AVE A : AN sendy winked ebb 
hy....0 See gag ss Pe An. Wonca’ Dick Baca A ptrews ae is 
pow Ove a. Cnerr- seekionw of Ake A he at ie At f 


Oo bance of Ahe prom froma Rhee Vsewbet ap bbe whats 


he, oy Kae ew 7e) Mean ANve wake o Liicd oon. 
es ieee Fieaaal pony een 

hie Aotok nrtrintonee to Xorriow of *he Abi S A Ae Rite 
a a We Keak AMnormmen*» of Abie comcentrie Anaher: 
heii T= Artrita An wrtiok- q= ae S Shale T, 44 Ake oukride 


eee ts. Nake t= dr : 


T= [rvrsde rb = d 2at dr . 
whe expression, fame? de wa calle S the Polar MHtomenk of Smertia 
ond on a Say ASS ahoft frrrde = 4 ar", 
Te KI = Bs t qan?. 


Z 


, Dropping AQe aha eine hate TNA i represent Aves orbs] 


tox ficient of shreng th of Wnrbentiil Ao 


=+ afr? = 4 afos . 


Bee exude, teaibte tee akinSink tn deferred. by 
Gun aittio- fet. ADB Ao AYee formebe of Ft. de St. Yrronk’ 


“tia | Le found te Sia Thomons ; Goalie ee Nokunol- 


qt 67 
8.108 
G 

* 


p.168 
§.108 


; paipacidinndien® te Dee shicueuk Who Ta: Gy faces AB, CD a skress 


36 | 


PRL ‘ 1k ed. ee f.F45 . : 
nee bowing ro kle given be Cotterill is tahew from ir : 
aesubes . : 

RELATIVE STRENGTHS OF SHAFTS OF THE SAME SECTIONAL AREA. 
Form oF SECTION, STRENGTH, 
bsrendars..5 Kh EMS eS / 
SG RTO soo a as hl ne ae ae ee - 8863 _ 
Rectangular with sides ire the ratio 7:7/.... Va Seo A: +S SGS 
6 Ueproe with acesin the ratio n:1........| Vr (n< 7) | 


ELLIPSE OF STRESS, [éeterizt §.199, nr, 087]. 
5 Ainge Nsieidie ano Counyrer IAOVL Lhe direchson 0 | 
a ae name for oth planer, bark aka avktensity ei 
Fecoming Gero for ner porollel Ao the force. In a feecnvmg ALe : 
plane Auk the direction varies; ow one pair it is mommeal, 
ww another Kamaewtial [page 3 of there motes), 
PRoBLeEm. & covmshelaen a pow of rimple Aomagitudioal APN? the 
Sinectione pf which one ot right amexfes and Ae invkewseiae 
Avan + Nee: accuses Re Lor Aentiniovc cy bike ore) ‘ 
sens — 
det » same 2 pooper e porolle trection-~ 
of rhe skrerrers ond a Connider a piece of POE or a 
zeker AA ) 3 thre prrers Le wncforme toh Aize 
Lek neoter bies i ANS hee ee 


T= 
”" ti = os » " ” ” sae 
ok 236 Se Ane Shs Lek ABCD aL. wii 


ae Av Xenra and hotal Danone AB sole ack ; aw BC, 

f ce Lt fe ewer of Sr eee a Dont Aotol »mownk, 
‘BC. PE gay er 2 neh wa dia iedeal to nre AC; 

Dei with he ianibney ae pobre jrshch it AX On, 

fo) eek Ao detewine WwW dinreckiow and ocegriteade 


wmokes with the agid OX. By changing the Length of one 


of 
4 


168 © 
108 


3°7 
4 of hohe aides of Lien reckana be Lee angle Mites be mae 


natal we pheare : aeieand tena pete Ow 2 31,02 frat Pow the 


Me = (fi-Ju) om tur O. 
Thee nasal ring atkrers 


mmialet be found aie Dree- 
S“imbewsiby by 


ttt 


k. 
o 
oN Jy 


ae co aoa ere /Le- 
pales. baad an ern 
Ao cee ae atu ed 
off OS=n amd Or =f 5 
Bate Danas Rig ohoouates 
St ponrallel ro oY and 
AR ponrallek Xo Ox , rhe Aukécnkit “oan RT Shes 
OT = OS 4009 = ‘eed 
RT = Qo su O= Tee 
Sence vt fo blowss Aheat the Anakamaity of he Be Ne a. pre 
L a pepnerinted uy OT and that Dist to Say RT. Sf then 
AVL — OR we Ae fo Ae a nerattont Arners an ALC w d- 
partion: ond mogwitude. St wilh he readily rcew that R fies 
ow ow ellinre of ws Bich ond , ore the Hie ite dances OS 
att: Ar eabies Ate Minee of Shtrers. 
J AK. Artntrrtr : ee oppo rte Aa nN? Akane cone 4 Ant a 
Ark off es tf, opporte oF SS Seer, from OS idea's t ee thee poink 


She Loewe of the point R moy tbe hown to be am Pine 
Ahices a AL. mokrow 0, Pe aes es 2 a ee few Awe 
Anonse d cs wh os wos : é 

Qu Ak we etree d lipo st am A SS % OU RinDAades 4; 
wn NaF SOM SHED i As ‘a ever ; AiidA ARe rth ALe 
“eed oT Fase 4 ae d 


Rial AL, eh Corte fr lfMes aimee TE ae 


HT Rg le 


om 
.. 
XZ, 
eS 


Tie 


olftttittttt 
y 


38 


ay We. CM eres oN Ae figure ther 
wy, 4 
Rew kan oe ‘eorevladabaoit* 25h a Ake 
AOme frome BR 
For. OM=QM=mP = TET or, the poink m 
40 Salt etuee Detwwwere ee en ; Once B i 
aud OV ake anon teh Le Trianabes OMQ 
vy ened: SHER! Gne oiwwhan, 
 RMsMSs= py - nt rR el oo 
whak Ar ee. vahie itistebuka sean RM. 
Sinmee PR=PM-RM = pal pe = t, 


ue RA = EM ee ee ote : 
wwe nse Afiak \Rovteei avalos is ace 
vA > oue of Ve pi Perse mage Fr of Sereribing Ow Minse - the pom 
¥ is Rewk aw anw of x anand AD. work. Q ow AY anes 
PY Meee ge aa Jisnin Akh e ' ; 
We et -P Teakaie RiM’ = 4'M/ = Pat Tez Tats oe p Rass aan 
Z z 
edie tuations, tetas one: Abiess ch denne eee tom fues~ 
Aion, tak a2 Rove opporite signs, we get the same pomt R! 
which < given by the wberrection of SR ond 2R’, 
Bumee R'Q'= [po w+ tik =f, 
dnd RP’ = Ht Te het = Ty» vty: 
Re BP rhe Loants P’ and Q’ ore Rept Ow Ahe aner he spout R’ 
PEND + 2 Sarersbe AN Mipre , AQ anethod frequewtly wer 3 


Bay aaference Ae ae of the Lark Awa figures ave Aee ARotk 
OR*= OT'+* TR* or fe = pean" 8 + Am’ avd Ainee Cis the Raden 
a» Vx = " Con aye + SCs NPL Aa Se ; 
Im the triangle RMO, sx RMO! ain Me SOR: RM | 
bux Afe angle RMO= 180 -(RoM++RM) = 180° (wx +x) = 180-2n« 


t im RMO = mn 2 ut Aim re = BT, pin 2K . 
ip z 
MAY Se ond, Ain (200 Lux. t*) PE 


V 5 a of Pin tae Btarerrer bu a 5 x Arner» a 
PROBLEM 2 pro blew ov akakeo ba our thor” a rant 
- ne More vacdal prob bene Ao Ss Rate tak 


Fae 1 Me | 
A tH “B » State o Bknerr Ann wo Di: wud anes aia 
A le 5. obvougs be reduced to a roan oF AA Arknwrres 


c Whabivin the stresses mar be Se 


$59 

ee a ee 
108 aM {Meare > OW Chicas 
nwt be equol and RO is +e 

Let Ae az suet, Aomgenkial tamponents i, of antenrst 5 
Baad +he cee components Avternrsitrier ca ane Aig 5 407 ake 
ES Pes equilibrium of the triangular portion ABC 
‘ ss AKnes4 op ces $e Yow ued Atnrerr ; 
a exe akrers and we rvrobre it“ norollel to 
14 t AB, for De component provoke? Ao BC, we eee 
a . PAC: e028 = q BC+ TAB 


as 


‘a 
~ 


| pie eo * Viet Tat 

“a “Pn f= 9 AeosO estmeyesres IE S2) 2 SSL) 
i Component poroltel to AB An a etre a — ave qt. (8 
: Hoobeipba ing equabion AP bu 24. (6 ) awe ane 

a -T)(p- =a’; 

Bs rhe avoot» of + 2 eon i won 


1 5 | 
fh = Tatty A oe (3) 
ne aE lB 


+> Ts = 9 (cot O- tan ©) = 24: cot 28 [Cé pl eg. 72] 
= ann 20 = ae eas cot 20 = ea a cere : (4) 
4 | SS eae obrwanys aves Rie) ada Pease of 0 akses ALiot 
be Bs Lanes ey, 9 aca lt anales gow, ofusanys @ O”AMuUVY waaay, 
“j Bie. akrvers Ar Bs do Pree Bet Le mow walkie o. 9 


i nd atta ies Tene avo i win Xedooh : ate 
| an 4.38 ,OR and OE nAenresenk es va AXArer 22>, Ww ob, 
OOF is Ake diameter comjugare esOR?. 


. 


ae hes 


i 
i 


LO 


Pro whe Gwen hwo consugate tresses to ford graphically i 
principal SLTCSSLS, 


Ci 2 ag pa UI na oA ANE of the Aone Rid Fig, A, a8 OR 
and OR. Jake Or= OR, , Birect Rr ot k j Ane ae ae 
MP= MO , Pand Q ore ayers aw ihe hess Sane en ae 
Ae eis. “tthe fi = RQ, T= RP, 


Rewitw 4 co ake ethene Miia 4a Wammwrw ok AAd~ 
POG RM NIE BES pre 


ehocrg Gs poimecde aus ee jrorwk M Be neheieie ae O11 ALe . 
mea Bnd came dinkantk from R and ; Ae ae ADe cons tue 
iow, m d : 
Whew AYe Aknrerr€> ore of opporite Rinrd ee cow, tee 
tion a0 ar shown Aw FiG, B ; Or =OR’, Pland Q’ ore powmrts : 
ow BS AOKEAD , = R’ Q's = R’P’ ee 

ne RQ’, 
Fivip PRESSURE. : 
woes ne rtrerrer ore ee ree equal | 
wktenrky om 1a fe Ren ake aa ahh: re 


Ons LOW (2) the onal RENE Sida BBR ve | 
ee ied 
sf oe ae ow . 9500 planer, aud i ireckiowas 


ORs rire AND re ira STRESSES. 


Wr = feels abies, a agen es lls 


4 169 mre. gee ee Was congbes Sie Grn Ae news On A ee 
5 i08 Beak ko es plane ovr be bn ie ee Vag oe a) of qm oye al Atnas >. 


. FRICTION. 
fq oe hs 3 Be fi a a ee 
q : ote Jers § af N= PeasdS, 
BC i T= Psi = W hon BD , 
a u x Gra ey Un ~ FN 


. | ~ (= SEBS f. 
i) . anc. tan £ An calbed AG, anole of 


ie ~~] ond “5 é ‘ed Dax: 
SSaaaaeaay tg oo nega sA tno 
Le es ae woaia We Axe a Y by ane) GF ra 


Ann STD PR OOe: a Oonv AN p) us 
one "ae ER Ye. hodu adele qraok “phehe Re ee ae 


Arie poet, Ase ee ; 
Ani. g FiT= fn = Nxang = ee To a nt Sa 
Yi+ 


—— 


es he £ Teen ucaeeme Arey OA — 
Ara te ae a revo Ride ee abd 
Rison £5 eee | Sa of actiww ane 0 
mwa one ant [unier? ah =e pevratle As, 
prea one wo ll ee A oe 

Bnd ies Fines pe! A,B, e 95 Tay i 
Im Ave (94) ose “WH ack 
Bae eee 


; Jere if fn 


yaks Weve 9 he tniamade 
“ABo eds ones be forces retin - 4 te fase il DANOW weg sig? 
eh Se a 


france (gsiags 


nae i - 
@) each 
Ra eawar 
oo x : 
~= x = -R tat, -R, toot, fe Ry cost 


42 Y= +Ramy - R Aw yy, +R, oma, 4) 


‘-M= -Ry - Rim, - Roy ; 

A ey, Mie, Asa See of R, coat 4 R, Am eke, ane aperte aw Ae dacaate 
3 25 prudank arroutd veruty AL first Awo of Ae eis LOW) 
Ve ann Se Pan wed Wak ine aan, AX aes of 
Aeckiow? Me ALG W? of R, R, Ma we mort AI ‘eee Aanahionss 


(1) are oloed: . 


Suspension BRIDGE. 


2 Lig 
Niak xr = bmn oo we Ar 
ALe focal dintanee’, 
waa ie #. -- = ae 
41 


Paoarem I, Swew Arar ™ 5 
Fou the pork Cc, AF cigee (ae Se Mel 
2 ee fam -¥4, > %&= ne VY, 


3 Os x, 4%, = fern (V4, +042) .¥am = & 
| Anis pa v4, 33 “yr 
She "3 ie te ey ON ee ee 
V4, 4V%e Vy, +14, 


43 


a 2 . 
+ 139 Whew oan oe AMR Jae X= = = a ame aie Saas (G.) 
$425 


me Propiem DZ. Im We quation , Hom i, = 72 Seis Sh Se nbs re 
a ie of ¥, % from aq, (4) 


ProsLemw TT. ae (3) = 2pw , Aub rkibuting for am ats rane 
ane from (5) swe ae 


H = Zw = a Spe Pere wide ate nee i 
i ial + i 
Ros Haeci = HVit+bwt ard ¥') 3 R= HY (1+ buy ee 5 <a sele 
be 
yy : y. fromls), mes im } = 2M = Wad ) ma R, = HV (14'S sere At) ‘ 


PrRosLeEm IV. ave faved yi ag fl Curve, 


tolls xis homey - a = 
pe {i+ Sh yay f als : Nene wate (a) 
Aet (tomt4 M)E 2 2 -v Ses ee (4, 
A= Peal fade ‘fedy) = = Ee zdy .. . (¢) 
= ee (b) brant 4%" = z2*-22%4+% 
eee 2s 5 - im wer: pee 
Auk rkibwcing 24 es POPS of dy aw ee Aypretorow fz dy AI’ 
Arawe as. E (ete ted fidan tat eromtog z , 


from (8) 2 2 x4 f(4m' 4x*), 
wo ze X84 24S (bai ox") + hota; 


ee 
= + SY oney” aw tog. [+ a mtay J + e 


1m 
Arce 2" = bag , = x= Aowi , andyi+ ¥ X= Peel. 


ee ee m [tant ALO L + Frag. Fog. (Lani +Avei)] pie aces Rae (12) 


Ad 


o~ 
\90 Shue makiow , aw Lue rext, peony; re” preceds (12) 5 
oak boise Fase (d) Ay ou ations for “ arty w 2 : 


s ie forz shan forg oor 
developing buy Mie Bmomial Teor, 
A -{[r+i ES (4-1). eto dx 


=f de (is tye ayy - a, sepesee] 


. RE the ratio % i eee fait as aga i ay, table dt atretehed 
Aighaly sel Maocear mag bette thn Ase tev jmwsa boing “ty oe A heaves 


a= fdx[r+ tee] =f de + St fot 2X43 My Pei 
Beginning at the origew, and making 4 « sk See 
4: ¥ +34 prcanhy , .. : io 
Prposrem V. Vmuok he remembered that the peinks C aud 5 | 
eA wwtrile Abe SO A mover ; ve + Comotank ; 
, hamge very Ninlkes eid end tance 


PHA A ojo is Mighe cee es 
Pada aq. (1%) A+A,=a +3 (4 e's) 
. A(A+4,) = % 4 tt dg + 5 i dy, e: gy 7 5B +%)- ess aus 


T1921 SUSPENSION Bripae, S20oPiING Roos . om = focob Diatcee qrrrcipal anca; 
is , Pp . 


$126 


H 
' 
! 
! 
1 
! 
! 


45 


H+Q= (= oe = is vita) 5 frome eq, 5) a a 


et H+Q2v(tm recy +¥ toms) ie... eee AEE TE peal (10) 
Cort = ™ = LZ) x. i con) mA i= aac, too(%, toa 4) IY. Sela es eae (11) 
ee Se 0k anaony 5 AAR Alak's pe ES ree of 
: ies dak bie . A Aro aw tenllon Xe the ane 


et Ris are, AB x4 em {tan treet ~ tom’ e044 fae. eeejo 


ot ia obtarred Ay eae wr Sa fi 
6125, pee, : Rigdon pskanes AE «= ery “5 


2 mn ‘* BE « ts 
2 ast % 


oe OAL AB324 eh eyeuts +% be ikea bgp one pe eee) 


X+ Yr) 
» Derlecrion oF A FLexiBLe Tie 
=! ‘ \ 
ae DE=ZEF =Eck = + (BC-BK) 


BK: Be: SEs be 3: Ps PHY 
3 4 wes 
BK = BC Pow : DE st (Be- Bc ae 


ee 


ee tit i) “ 


ie , 
ce.) 


ie soos . , tyza ae 


24,2 ADC, az AC 7” = DN. 
DN; OES: ABLAC 
DN = 48:08 


i) 
Apc. ac= & AB - oy 
3 Ac} 
Zz 
See eR. ge ee ee See 2 
ADC-~AC =, 2B. Pr) (2) 
<> or TE 


fTHWITVRROTE Th 


Se forces saaendae’, ow Ye qorkron 
AS ve P, Ry H jain hake 


toon = s - — ! < 
_ eed copia re 
me ao Ree (&) 
ee H pw we 
‘ ge ae (8) 
a tenes 
to inkegrate BS ae hace fone = z-A Ed (¢) 
mr. net “2 2 > 
2z sept a+ ar = ae ol 
2 wee 
Pai. ay Az ni + st Az 3 Az 
Z 2 2 zt z 3 
Viwt+a)  z - 2S so 
fe Dee (ht ere ee eo Az = Qe eke 
ae | Tee) ae ae 


ste = = Log (A+ ounter* + C6 When X%=09, 429; -. ed =~ togaw 


We 
Fs i Rell Sakae Tpit epee: FEL. Res ols” am” 
cot 1 = 7 corectt ae oe ) de eh i ; si ese 


: y= [lomte at) todo = nt+rt)tg C. Wher msm, ase “. C20 


OF om. equator (a), = = Nog cies my a Sn Spiga eae ae Bee ee 
os Vut-mt?. ey bs tw 
a = 3 + Hj oe 5 ot £ -4-=4> 


* ed 
Frome “4 (e@) deere log ye Jwiyn? = S (e™ + & =) 
2 2 _2y 
ea 4 em 248 ™ 4 4A” oe 
wm wa 


2 Zum 
ary ig Se ’ 
ess - Lins) oma Se EER ee +e) (f) 


Ok Abe pomt A, y sm ov. Q = ww. 


wet XT =OA=>m™ , 5 SAS BT7= Ga. KT se yin 24°; BT ee ee uy 
+ ow 


: BN = BX. rec XBN = yAcet = my. BN : from gues, BS Anione, bes BxT 


g ae 
| = id BNX «sve ee 


oc. . Os: - Bx* _ 4” 
= ae BN = xX+ = 2 = Cv neece ee cect tree eeeeees (4.) 
Agana ot S., : “i 2 ri 2 
R=VH+P” = a (vm i ee (2.) 
SEV PROBLEM set Re tant iG = Bo dee: SS eee mannan, : 
| —* ay ee a Oe 
(nial B+ h, = Ae hen x= s. > = = . 
kik ee kf 
A, +”, = SE hoe | tom ES i 


R ano v= 2S ( €im_ & B.)( 8. E-iev (Lt) 
x ¥ x 2 
: had 
VB. vy, and better be 
“alipgeeb cee x thar frome 3 Set k i ae Ae Ee 
AX’ though eguatzons (3) anc es ‘i (em=248 1G: ee ee ite 
(4) will b¢ the“same tn either + 


Case. 


east he (eh -2+£=)(t& -2+£*) 
§193 Bu odo tractiow ake S og (= - es | = ).4 
se T-v' = wma (EE ies ON (3) 
Bddima ey. (A) #U Li wm (eh kyo eh. 
subtraching tv. 2 m (ea erh..).2 ¢7 
lav . hee & . {hg lev Ue on Vos ewe 
1-) ge a Ee Tov 
LF t= (om Raye bg. Lew 4 fe) (1) 
we sri (ow gp, Log. Ge f) 


([3.) om Lm a ay lwo) w 
Hence : am [I + x, + aa i ant ike Ac 5 a ere (k) 
o . F ; 
She tanaka eo os qonebola a ky focal Surkanee = 7 w A” 


rhe £ he CPumze rhe deo Are 
dugew vemg at merken , en . awk © 
fe) SE, a Bae e 5 wha sitcom al alae Mw origene 


for Nee cakewonn ; we Pave ‘ 
-™m = nyem( tang) Tish ae (L) 


Ga get Alls Length of tke cabenany Wf a 2 2 a= cele 
fund walue zt from eq. (lt). A =yfit Ft Ss ted 

For rhe porasa la A= (Ti+ Fa.) j from ta (P) ne ee 

42 {ie Gt) es (lie Eh) dy = ah (Y/R ae Expand (w're)* Fy 
Mia Sinommial Arc & inmkegnake, sw hich gives tq, vm honk. 


PARALLEL PROVECTIONS 

oes Ertl Vines AAK OL 5 
Me | ougimnad RAAWI Oe” woke 
Ace doktked Lanner ‘ko Pe 


oe felt 
a 5 ec 


Bie ed 
7% B! 


rou tates 


ae’ Se Aawmer- inatd y perms 


ee ae 


a horter 


am fo ee Pe ccd ie es ge ities 
igrusieele tg PBF gs Be ge & 
: Ll p eon Am suaikren/ Qe. 


eee: ee “iets WR! Am PR: Sa pee ony! 


: take ae 


R’ 


“Ae uaa As) 


TRANSFORMED | CATENARY 


:. u Ohg: the exec ee (Fig1 ) 

. ss erg. 7 = amee te pation RORD 2 Ans peat 
Re iw ice tambon Be wide watlenuis 
DN. - Bur the food ow the ore AD 
| \ 


/ 


x és 


Aunpace = 


Shee aw 


Ar, ww = 


ee 
ee er 


pomt dD, T= 
sr ti? av ie: prot Ms e a. 


Br iw §,/28 vig. + 


on the wees ie ak A meres See 


7) ali UALS 4 4 } i Feing 
Picstgai Henee a tie. 
enka AN toa 
See oll AANAVO DE 
ies CQxBAC bounded 
b4 ANve Direckruye QXx, to ea 
from Adve Cnwe~ 


Bes te: 


eae 


panapemdes 
Lae ASve weight me: By Seu, to. mas ak” of bs 


Ov Av 


hp Ex 


AODE Sead td = wma” bas! iets 


he aie Mea ore AD. So AOBX seyrerentr pS ee = 


AxrAsO “ns = ee wrt, cf = mnary Hag 
Be Or ee Es 
ew ae, ‘ee one rag isete <a av CAB, 


scion ak Sema ef 
Sate itn aeues 
ee we ro tag Aame 


mnie female of cue = ZF a 


50 


4.2.01 ww thn oni et (S$ 9 131) UWL Foe Se UAL? be eo Anton Av Yaad per 
2131 rae fo cble Mv Ye Since hs oie = De aonrre OX = AP : 
%, Le bad bebweew Biles Bs Pes «tOAXB = = haer: = P(e : - Ow 


Ainee Pi He Be wus ph = ot ws ag et Fe ee 


vor haa holloves, yes ARIS rr wre AUN fe 


A0OW) of $128. 


+ Sa Lave the henrion otc BeyvPoH? = wn antes phat 7, = 


-z cs 
wan (€ “+ 2 *) Sie buietey trie Cie bes caus’ wins ha ev aaa See a Oe hate ee a)” : 
+ . i | 
“ alee N dt cela ae change nw ate Porm. of 
| re 5 se \ 5 ig ALie cuwe AB to sarmeare or Bowe ‘ Cee 
7 pate a8 i he en Cer provided Yue proportiow OmMow 
ae i | y oe ~ Rae zz) wwe, Note _Araw ever, ida! 
: / Fig. 2 | > i we samnot Kramer Ate depehe Ao of the 
cf 3 se a ne negges+ RB Miers eae ek, ott 2 
! 


f \ Hence PD ee wid uae (mw = Ao) ) Peres Qe 
on jap ov, vs if we arroumve the pate Ale modulus as Come 
often interferes es & 144 ANB of Ade Wm wow 
vw Abe bub Soma of archer ww hie a a es Awerled 
Aan ae Ses aw Pig, EB Ris nucekol pack MA neplaced ao wall of 
ow ore and Abe Aarnriow ow the faint Ao ney baced 
We ore often 4 nighties ie mae Amey Cnrwe parr Afro 
AN nree: poms , ar br ¥¢ Sa wohile Ge wlibent Ha 


sa AAMIMe yer = rare ware a Ae alent fa A 9b 
dows eat spoons ther ugh ALe mesa & 46 g. 
J ouercome- BRS eas we a7 he Ananiape Anes cate ~ 


amet, ALA se Pare, asi tia » Ate Sek 4229 of ‘% gers Newaw 
¢ } 
wa chanaed a Wa Xe ee a Lees af wy and P ane boa Ate 


Ane wes bf asin : Up, ie ie poet 
pa seh Ligte P: Et fs ia aly see] 


, . ” %? .¥ 

1 ets Ae 1% a tq». (4) § 128 196 {y = (t+ Sees be 
Led . ' af ~ &, . ) : 

‘= wit, a g's £ eC ee 

rhe Lous wae ee 


5 geome = hg Fon, H's H ; P's 4° P a 


5 | ae 
ol Ju he see equations Moe re oe of tare ar yok tea thie 
31 to fond a Ae ; eM éq2.1)?* § 128,196, 
\ : mw m tS mm, Yo 


Wr = dog. (% a I 
ry gout Hee caterers CAB pF Ne & transformed 


q ap fod the 38 kease of Fe ethene entation khee port eae 
7 Bee at = ie. (e- e*)- 


oy 


H dy 


rl \3 Sassi’ Pade EO nf ¥, 
e = 4. + ot. )* z < +e (em ¢ )?| 
a. oe tee 

ic si | 
.) ee pape Nee of an otk a 8 Ft le ze); 
— Mune = bh fe. te mina) } Keng hut of Ci shictale pueds Alea, Cronin 
q = L$ bk, ‘c Yo) ; ws Ww. Ybr., ae See FM poor. Canim ALce ; 
Anam pormed tadieavonig ete ANe amon and Aw bine chion 
of the Alrwet at “the abubwents 
Ouawer, t= 64°05’; Hz 6359 Uh,; Pe 13083 Lbs. 


ot ae 2 owned Cakenranrne AD We 10 te ode CUAUrve Ao Aaya 
a. att, a” Pie As Ke pe oS zomiponent Ao Are AVAIIMAR, 
at ut ES ek bo do purrore ide like Sie eee See 
203 Cracutar Rig FoR Fluro PRESSURE. 

133 Oa flenible Maas Soke peas acked ow tu Ow amifor imensee 


Arerrwre with _ arms we tinerlon croar-rcelion, 01 We nner 
wilh be wnfomn, and ko rerirk an uvifow 


* Uy Sie wale Se oS ihe circle re) Ye ee) 
ras LWA ote wk ills Avian sorrtiow 


“we 


a — x. CAn Bae Pe 

; a She eee eeGucest arms on as = 4 da > ee werki beck 

d Com mew = -Ar: tor 8 ls av, PH re Fee 
Ae fin ) 

oid ins Mee! Adank dy = decor 8 ; 


qedrcos’® _ 4 2 rdrrinb _ 
Te eee aa 


Yc More fore the Livean Pavey arr he 


52 
204 - 5 & = | ty = | ey = tyr ee 5 is al H = P........ 0%) 
B38 Tk we avidenk ssithank iatignakion Aak the Aveta 
3, VeteUne Ow Aewi- vy inadens nary i Ake AWMe 027 OW OV 
to Jrereure = 2Psamr. 


Co Plaid Avera Are 4.40 of Mere Nokes . 


- 
» ‘ 
§ 134 ~ srg ceeron fo wsss : 
; Dy \7 
ly SS S> iy. 
y gn of Fo "pay pip 7 
| #2 te pe y 
aes : ie y Tae 
fy i | : Z ei Be 
Ae yon i Ly ott or 
\ 
i\ < i 
1\ hier oF | ; 
ee. j eis 
ae ; B<he: : 
a es ee 5 
x’ 


p= wabenrely of pierre Peev, original Crrck 
¢ “fs ; 
P’- P=T= wr, H’= cH 


, . ‘ 


“ 4 ws rT’ ms oh ee r ne ” 
Popirin . PPE = Mts nr! folso PZ pr’l (3) 
Pe Pe He err fs at ee 
fe es OL ES See ied a CH 
7 My aS. rag NS OB’ _ RE 3 Ye. m= --e02e 2 © eo oe 5-9 
Rte a On \% (38 


) { 00 i os Y. ‘ int Ww # 


, 


p's <. Bak, ty(3/, Pa pr... pe phe 5 (ve = ae nevisei net -. (6.9 

"e + 4 a Foor Sh ys a pee ass - A a i 
Rar Meals piskobion satacke Ave follows, a confucrineg in Atak Foca 
ures Pp for Ye force jaar a Danaakiosns of  aohione ambewnatg i w. | 7q 


33 


O. : 
4 oO y me eymatiows (51% (6) : 
- wan O'A'=1 eee: 3 B= cr 


se ake dvoame ters Ao see 
tre quis era oyrys A ond 


=, ond ther omater posta. 


ee Ly, (>) ony Seki: u 


“EO VIA 


omaodly ic et | 

Ae gpeprcal LImatAnr ie vag 
Fae paw AD. Patek wu 
he Oo torraek een bs: 
Pde lve Ariana be o'R'S 


= A+B =¥ (+s Ce. 2Tey c04 Ji... ..(@) 
from Mee. Aniomahe O'Bia A-8 V (+ + Ort ar er con} );.  (B) 
~ = ALP deh =F r{ylse i 2E tong ) +70 Parse ie a! ae =F 
Bs WPL 4S Ra = Ff{¥(i+ets 2e 107) ) - oS h8 2¢ yee 82 aeC 


ae Onabyr. Gown. {4 B' Amn (9-0) = AB A'*4 B= AX 8°} : 

frome Aha fg. at Seg Ae Arcew wee O-O= Co'A' = pees - Amn (0-8)= e004, 
a : B= cr st T CY wwrs = AB, , 
Trey = As B. 


hocking ALe fect , eephiay ond aad laine ye ager eqn, @) +b) 


¥* 2 L= Cr coved 
oy b.2 dand 8, 1 pa aif; Ain a Aww ol 


= 00.4 “o. Ar d SiS he Won eh re | 2 Sa ee A*=B- 
ee geet gs Se Ae tO ae “Ret 
Gots Pee Cee “ed PPE LTS Se On ey wees a nee tees, wen (6,) 
: cry Ata B* 
B52... St OT Min 26; buk when CT = x Maw 2728. 
Ba. SO-a . Aw (3 = wre 


“age a con el 4 |= too " word spapee Bee? fr ois eee 
ey* At B* fae: =F aroe 

a 0 lo HYOROSTAT IC ARCH, 

a eer eee a eee 


oan oS Pa (Rdye w (bd bday = Toit G) 


\ a 7) 
pe H = oe = we [dy sot Seid dies bags (7) 
fers - ; “P= a 
Jee = wo [ade = ase se is =.T tor v...{9) 


x 9 Y Water Surface 
> aon | t 
: | : 
: | a 
ae ee ee 
| fe ea he 
j nm : ab sae a Nee _- ) 
\ bi ¢ ae “TN 
/ Eg “2 of ne 1 
; * aS. 8 - es | ; 
fee oe / \ | 
2 3 ‘ f | \ H 
' Se : ; \ ) 
5 Ht ! 4. | \p Spring ing Line 
: d K % : F ' * R y 
‘ ; : ' | 
rs \ aK 
; $s & A: Mn Ni 
| VX ~_ IS 
: D D 
ae x 
c | 
ws 

St nw } Centre of curvature 

(as OM 

B+ 


tt ae a taos. CUnve ra acennroarte 
srev0ome ANue Pinre Gee Ree ARMWUOKED AMete DW ON 
KWnver eoinede ar AA Con Ne einai: 
PROBLEM 


ee he. RaOAE 2 


Wn 


ellinre where Atni-axrer “se oh ¥ = y+ eget 
GMS Gh + te =A 5s Ae 
° ' Qa 


aoe 
Auk [pee fig] ¥,-ko=a x, (45 — i) = a 


Pe —(1o)_ { x.¢. am ae % } “ e. 2 “re xt 


_ Ket aay, + a -¥, 


2¥, 2x, 
2 * 
LaA%et+ Qa a 
om a+ — 
2 z é ke 4 Zhe 
e.= Ki~ke KH, +2 Ay,-a Zan, ~a™ b= da a* 
2%, 2% oe 2¥, 


MB. 


“1, AYok Ai 
She centres 
gnake at te points A ano 8 ave neo 


Dlrswnvineg Lok Ae RAOWU 0 enwakure at AKB me 
( : 


a ee 


“iGraj 


b=y ts a closer approxincectiore un the curve drawn above than b= Yy, + 


eo 


— 


x 
Zon" 


E ee 
ee 
22 GEOSTATIC ARCH, | ee 
ae wos 0. 
£5 ‘ 2 Cals em ‘ P 
‘Saeed ae ee H-—er me Pon aft | 
ee : Seen eee | aed 
| rt y % Se, YL Z on aa of ' me : 
“ ka + 3 a ae AG cE as ‘ | 
us $ & 5 * ff Hi if 
Ly if i st Be 3 I 
if \ x ! iz 8° 
; | 4 tf pee { 
ee ee “WiGR ME se oe a —< 
1 UJ t t.. 
leg. 1 tt Leg, R 


4 > - eieosAr ae chro nee Rice Bee a ms qrowe xs horizontal 
B Ad. aa Lier: 

r. vig ed - (a4 
q Beiweiaht .o ae siarvirke x ie upeee Gor es A 
a SS ee oe iE way! j he a = aoe an ae P; 
gq - Po ew ey = a ee (Bb 
J ie cual ML jroyeckions P, re on Wet 
Bilao coals eee a we: =eP=CH : smee Pn ww 
the Kabove eh (Ave aww 
5 HH’: ¢P’= ec PicH. ee 
Bs, ee = : m2 oe es HS [toe atic OPE Pye 

Hl = $f yh - but Pee Ce = Meee Tt = = ¢* 
Pile = fe | ae rd {bat ta , i eisiceins Sekt (1.) 


Lk A aes de CARA 
q Phe ibove “eo ayylreabte = “hag : Des ee Ais AW, 
ter of the two: to Veadita ie , 
* Piz ws dy’ corny , Buk oly’ = oe 
4 | ; en C ton4 we fy SS OS A te EL Re Ge eee ae (z.) 
4 == a 4 ae = 4 

H'=¢ P’= phar ae oR ae bocca OR ea aa a oes oe ee 


MM Tw cree css: en fe ; 
| Pa A a a) c= 1a} (1) 


q a (1) an f whe Awye eS) Lo oe Or 2a. (1) ae tees he 
| 4 Ob A and C’ wu A Ahie Ave Aes A”? — Or ap oy 


a 4 


4 AT CROWN, H‘- Tobe gh Ws en, Ga i oe rasT ore 


p43 AT SPRINGING Pos iby ef = or = CQ - ; but ip eS: cmp 
S137 Rs TPC OPE SG 

©, ‘ 
fi : 3 é = z 


WN. a anes a eer ge Ran eave “oe he 
mok frolS whew the cow ate lone in 2 ma ,a back 
meat anevttivaed “40 ee ede, 14 5 


pia : ce Shae ed aw A LENEAR ARCH OR RIB, 
§ 138 ae G ee 2 Springing) ob. s : 
% i 3 : ae rx 
a3 ad Ai | Noa. 1%2, was Urratraty A 
%-« i H : ( 
eR ¥% id h /\ Pnian? Xo Annie sj nana Re Ww 


under Problem Vy 


Ty = we 5 he senuce 3 anne Xa 
fined re’ forces eka ak 
D we Lassie P = w- Owe AGC 
j | Hae Rorrgonvtal end T ie Anan 
eps A | Ser direction of AGrer kam 
Y Me % OXO es (axial we td 
Ns \a Grown | a ee re, t 
cin a c) ences Gn ation wy dam 
: (ER we Uw waite, K: 
H=P%4 = Peotamt ; nail 
Up a hae } : 
Mak at A Akane 4 Ae 
component, ard Ae Orca AdG 
Lian eta aaa ke zero . Page 
nonk co new - hee 
= dessa oa Bp rhe- We 
see se tomo ment of Ahan 
k Imenneares to D whee 
Hig.2) avd a wok: xo Ae 
tre 
5 Ga mag 2 aeww brow, 
wwe Reed, 9g.2, Sea Ruben y Rohit neon 4( 8). 
From B(6) to D(d) the rpandail murk puro hevigowtakls 


/ Eig. 


$4 


a pgeran’ a ilk Latinas DP {a ) tnd MW ak nak pull Porijowkall 
$is8 hy ana haa hokween Mand A ak practically oct een sur lhr 
Bet wl aerrta MAR A ; wertierl Lines, 
ak ye a refrerewtes 4 
onees etn aw Ake tte he we te ‘Didi esa 
Fy AM greater 2 eee fovis onrk co. went of DH; ov 
TiaW+RP RP = To - Beokant = the poate whch Ws acted 
prt 7 ke Ae’ Pe 3 Dekusaaty DandA , Jun Seq. b w= 8S 
-RP=T,-P-ewtani = purl Dg kestanhas A kD. 
Bee Sad FR eR nanerenks he Askar of off tetanic 
forces atky Ow Aue portion of Kee Ps AD. 


PROBLEM V he rake p> key To find the prosition of” 
the resultant of the horizontat thrusts below the nowt of 
naz 772 thrust. 


Ion Fig. the problem co to frond the porrtrow of re 
pier a a Kronixontad NE vaca e Setiiéews Douawd Bs Ho 1» 
Adee Army, 4 all AYrese forces and ANve promt of application 
abou? Bu amok w Be pmomentks ahouk O squat, 
Of Ade ‘arch finer ob figures ar from C Uren the park of 
H whieh tomsirtr of bie, Lonnintak ff aioe of the 


1 2 Newt At os 
% . 
Soeteee jou =e oe (s) 


Combe 1, Cotewonns Ke, 2° : os P totam 1, = constant “ ks x, (6) 
Evomuphe I . Senidnealans 2) Ce ow mo reranre. 
ts = i. a comotant ; H= pr ; ahs = p [xo = ons tot t,= 0 


ee EET athe MR arse Ne eR 
‘ah 2 X, 2 2 
eS Ji Huydrortotce he. T= e® : He = [nox dy sw Ro 
| %e 
%, mi. = ees x? : eS ¥,- x? ) 
a eet eee 


Exon tbe Sd And 2 wd bcwke) ALz avomnp ber, 
= Ms eS aiven ceheranse ameeevegniy and Kay Piet 


ARhee Ve) Ake forces ae, —===, 
“4 EEE 


38 


X= T(l-toot) » dye Taanidi . 
is Tame ; dn = Tesst di. 
Ne ie.. = cao the deigena 

Paw f(mrsy) dy = hice: ah 


Tv Coat 
= wr * f(am4 1 ~ cond) tori ad 


~ 


d or gk [fons wat di — lon Ll di | 


t 


, 


Sark feos” tdi = {G -Am'*t) di = L  (eichs dis. 
fader 5 ay = [edu hy ee : An = So aad 
( ow Amt dd j v = =~ on } 
Am*t dt = ~Ameé cosi + feoste adi 
[eos t oi = t+ Awad cori ~ feosts oe 
= fer dieht= Ee ¢ Pmt woe 
es 
- : Amt torr 3 
P= s+ Shwe) acne. y -i} tastes ible = 4- pl eau) 
ox : 
trom eq, (1) c = Peoti = P cose t. 
AAW ot 
We aon +m) rin Amt boar t} wou i tort 4 cord 
f( Amt F ~ 2 Fey Ter Tl) ori = -t This 
OHA, Sm saarge® { (1+) toni, — A" bz 
~4=- XH wr of 


-—~ CAT 
LAwt dt 
A{tewotid) coti did rei ole tort dt UL - Amt wrt 
Amit di Lami oli 2ZAm*4 Awntr LAmi +t 
: fy, = wr(t4m - cori ~ LrAmt cont MWe tae 
Amit 
haw. t-e ane. tor finan. Latret tort : 


: = Opynowwniate =< 2 Jin bbs (10,) 
Strom 24,(F) prib E = ben, + ee t= 90 tot 1.=0 
* He A 
ciara tance A Se poet li -TAmidi 


~ 90° 
y= My AM 1 (1- 00st) di nit 
2 


testes sone (19) 


Mt .227,228 SECTION 1 | 


b 150,15) 


T Calling We inbenaitny of the Qarigontal rerrure: yond a lath 

me. th: at in: iv Pe” Sireckion vf De ayer of the 

4 egtionden Z, [ree 4.4.43 awe howe. 

. H Tv'p 1 oR Wm a : oer 
Sega 4a os tage 

Re 3 = rl = Luv’ yr 
if T27',07 am fig, js ie pheaars 
Be = So, the od in 0, plane, the rut will Le imfrnite. 


eck = cee 


2 


a te Ol 


THICK HOLLOW CYLINDER, [see A.M. Art. 273] 
Kenoriow , Ov hoop- tension ar WX ann ¢ 
solles; Pr tae Pe epider jin swear 
| hy bind tescean, a approrimorele Anne avd 
© diwided nko rw Ne ip gs Sree Scr) Rome breed ee 
Be Aenrrdw of Neg Aindaaen ts foo Kolanecr jronk of Dre nadiol 


eee nee: of Adve co <a flair , Ao a OW radial 
qvrrunre Pickin waitted: te te Aecomd Tsop 7. SS Fran Cherefore 


GO 


p.228 tas Mas Aenriow Khaw the firok Poop and fil te 
8152 eq-(1)§ pil [p.s9 Aeter}, ay f bu a, to mate aX gurl, An 


% 


yet . q='¢ ees wes Ae mean Qoop-tenriow vn a tick 


audi of he UPabed) Bee Ole’ - eked sr re arrengh of 
Ahi mokerial "Pre object of the qrerenk imuertigatiow x0 Xo 
row a keak Lins Ake saniiioen” of Kooy Aenriow fe ors Ania 


: chases eine 
X-SECTION nates ratte .. y De ro lukvon per- 
fuels general, 5A al ae 
Qrnder 
Ap UIA AW ux aA 


rtd aie, 
% = sional = : 

{2 Laid prerrere UAE G RE A: eae Meminidins ak sone le te 
: 5 6 withouk ; in 7 ” Outer ae 


HS Nae coon ag ede a a 
‘ eae a kBok ri i Rado 


ww” ese : x as wone ¥ ‘ 

ametowne Due ay ae as Geksretu Ahn AotoL re AO 
witha and withouk, aw. dnestidw Sierlar As tre radius, 
ow a quod ronet Baunted ey Rok nadins . 9 difference Aa 


. Hs - 1 R. 
Comeceve Ae amg to be divided 


a! Sve {4 . Mn Carinae 
Saow A aAywmrk 0 ‘ ee) orcen acki Ow 
aver of Atness 0 ihe: oF munakol inicio t- 
cl Agha Uf Tt pen 
Ameckrow ; y ‘ Ar. oF eV, a 
> iadbuok yrerrunre, 1 (Rib for each. al we A 
Aunrfoce wa ai and for coeds particle or We outer punface 


4 
} 
| 

7 


6 \ 


’ 52 we "ear Saas ee our ve) rimcipal ankaerrser Ao Ae amade myv 

7 of Awe component pom, vig: — 

* A yor of equal hwies ih Ase teabee Riad, conrtibaky 

; o fluid Gr Fela a revs iow »>wWhore tommow inkensike, stoked 

: - ae Xo -he ans | ae seems a prrerrunre He ne magarinre 
j mw 2 pon of aknrerres “of pat natn iss ’ Bn Ae Pf a ee SE 


cA wr Vit aw. 
Ms awe Rawk: = utm;, p=n-w, and Ade ro bhew in. Kobe 
otocs 4 Perot A amg ~w Xo ack vibvahier Payor w 


Mm Xo ack Pek. be, Lar com Dining Auer Peeks ; brewing, thak 
4 ae 0 bglikianws — io sp heat (a) se Dake Boaniawie ) one 
: a tote ane Awe fou SS ae of Rand ¥. 

CASE 7 Equal and Atmilar stresses, ov wmazo, Ww pA aRe onre 


Se aqual Ao AXve Sroop-hevorow Od “eon ts obonay with. 


ek a Pluid hension [Hotes 40] of Que ambemarkiy m ‘ok 

Mach. soit . Equakiow (a) in fulfilled Digan es 

_ ia =i =m = a Le ad BOL Sy Gee ee ($) 

3 otf. eal cite oth ates tp uokwa (a) “bo . 
AD 


Case JT Eguat and Contrary stresses, OU m=zo0. In a. cae 


j 2 ea ee er Oe Ee 


3 ek ko SEs ie ge i, Ader of equation 
) ro a(t-4% 4 


j CAsée ZI General solution. B re: BN ASe Awo ponkial. 
4 potutionr > moakrvoas (6) and ef together, ae find 


Radial yrerrmne , mano cence 
4 Hoop- tensiow, Yamtm =F, 4m; 
4 So Aekewnwme AS cornmrkawts , aA anid mM , we awit phe agquations 
i IS Eman way 5 a8 ~~ eee ete she) 


; a 
 tubtracking the second from the first, 


62 


in ee ee erg 
< Mrs from qs. (e) a-T™ = pare ace wa Ree = ,R° ome pir" Vu 2 f) 
Ri-rt 
ia spe We final Loop Mipsatiiaondc ak AQ. WWW aurtace 
ol APS AQ O Mow | 
ZT ie _ (Rr) — 2, R? | 
= oT ie hg . R*-yr? ea a ee ) 


We an wranrrte ‘cane nee ER Mie sic 3] sa 
Pe , and ADOWR’ 17 M220 WH 2 : 
4) = pn (R*+r*) +p. (R*4rt) — 27. R*. | 
Rt ar. , e 
if sg cent eo bible it fF Ae» yy (R*+v") - 2p, R® 
= pits R*) hen, ho dir corcled pe AB Aeaver q.= Roget) nn (hy 


u p CAs: 4 hi, £ A” e 2 
Repta fee te e Araw = K-47 SUA 


bes a heel? ne j 


Ss eee 


p229 7H/CK HOLLOW SPHERE. [4.m, 275] 


53 SECTION BY THE Shaw fe MAR peprerent AW Ocarwediol see 
§) rinte ] 10. Stns ap hara. the Plaid qnaroune 
\ halk ar Lefore 7 | pverannre eo nts keoee : 


] thie | Aeitioweinste | 
RT a ; 
and if tte rection of the metal fe 
comerived +o Le Siwwded ninko om imdehamiberl 
Pennies SES of comeentbrue Tay , Ae breadrte of one of use 

fumnagys SS: dr, rks radians ¥’, ond the hevriow ak it q 2b an 
pears Afeak Yue total resistance of Wee aackiow wilh he 


an( Gr’ dr; ; 
idhannee! Alber Aopuakwor url e fulfilled for abl arin of The 


randR in a 
t 2 { qrde = pr Se eee eee (a) : 


an 


Som Ammaetay ik onyreors thak Me axes « artrers . 


‘ele onat 98 aS ESS OTS 
qos mun? e, one m + ineckion of a AWA, Ww 


63 


7 ops Spe 

4 Pt, first ond toeack ae ef 

e Yptlow if wo mankiok rglukions wilh aquol bewrions 
om aap WOW C/V ; MWe eo ees 13 


' 2S hs 
Ae ALak ‘Ve 
; y a =mMn+wm 
q Case T. a : a Si mw . 
ae t diester roll ‘A aie oe of fluid tension, 
ge dinechions it ee pty ltd eagstete 
‘ goally hot ee 

= ) equation 


“ whieh hadaces % a yea aie = tometawtk , 
5 oth. pid of hak gilgtin, i? itis aden Ace (6) 
CASE a ee m (R™Y') , 

= , a= = Wis bare RL batt Be 


ee Ai. care, ea (a) Mn ‘Sew £, anboel i 
he spate, (alt Rel ible 
3 "1 = vl 73? ys Re a nde (Cc) 


Pick’ yan See oe eo 
fa [pede = pr - 7,8 ye are ss aie 4 
3 re war R3 Py 555. Siew tvoed mena 


Bi. 
2a(h- %). 


q a a, na 

7 A aa I Ab og —_ —_ “yw 

q R3 PLD eligi ARE StS ow ae (n,- 3 

,. | 22 ay Mts Pe Ri” 

sz 4 20 - 2 " 

4 aie wr? oy fee Ape ineig S* (R az) a fe) 
Ri-y? ? 


ps pete?- 27) = = nr sie bs 


fs aren tere 


2 oa uy 5 Tet tr) 3 

; Nokrng a oe 4 fore - cece at BS) iene ae SR, MisNe. (f) 

with py, orp, we Te ere a ha and Puff oe ? 

 gaves d Sno re Aeww Dgiy? 3 

: 4 To (R aie ce. “2 
p(R3+27°) per 


A 3 2(R? - ee 


R : yet Loewe 


ac” HB. aX futl discussion ts beyond the scope of these notes, See AM. Arts 249-264 pepe 278-2 
. ; Moment oF INERTIA 
15 


ek Gh sed OY Se le nes AA f 
pT aeeree rank, amb ak nig ae 
A metrically , thew the expredrions 
frrdrdy = Goya «Z | ane wld the 
Heng genes os eee 


moments 4. nmnertia, of Ate Aunface hi Aerwiae bomowes frome . : 


amertin aerpeckwe ly : 
an, for y an an mans wir. own bg VOUWKA akrers Gree 4D 
pis 106. : ~" eS 
5 moment of ranertio |e Aakew abauk a VAD a OY’ 
wha, chon aly sot Satek The Sete go 
Jawsis | eS ; AD. poe Peay F* rehirred Ao [ A.M. g 95 pepe. TT - 82\ 2 


Snr Aas anticke [157] Ade Seviakiow of We untre of yeeraunre 
from ie ries of figure in abo ee of the qn 4 ANA | 
amd , wulers Mis Ar na patie: nom, (2) 42 mot akanet be Armes 


‘< f= Pe t OM, ow from éq (7) Av. 163 % 2 al ioheas 
sj 


3 Pp 
= [fe dudy and Pez 4.8 oe ae She 5 
* Ee 2 ae = = treS = 7 } 
x f Te + opts 3, I+ eh fs fs 
S 
xX p= f° et Hts ~------------@) 


5S 


52 She a ae of [Jans * a , fox Qe Crors- Aeckiows LET A morrA 


; 57 frequently DOr ww po ckiee one _—— aA follows. 
- J Recranate, l= =x *yda = an dy = LAyb + hy S 


Y! 


— pe 5 eee | 
a Pein, ite Se Aiomitlane J = ibis nigga Peele 
oe nS Lee 


ay SQUARE. a £3 ap tare op £ i a ak SO 
aa p aie 


12 


|e 


Circre, 1 = [ota dy = {Re r*dy 
REO ice rat gS a of Ate Pai Linre 
ret ie obtained LOA Pee of 
fej naaleg tees te BOS 
ss eae 


K 


a9 220 ie = 2m(&yt = et ; 


yi (feu {ie 


a ° rie 32 
4 ee SSS pr 
3 Biscee. ae ; a J eee ee 
. ¥,9 i. (®)* $ * ; 
2 Pat +4 no-one! 
3 co th, 64 oh 
4 ik ota 5 Aimilonrty S5Ree Phi eu cela coe see 
%S _ Rah g ® 
: mAh ad 5 RS, +i ae ee 


y Hottow RECTANGLE, + (p28 - i Jr + [2.07 £87) Seg oes 


yl = 
~| [E a ECRR=EE) GRRE RET 
ae ERED RM Ee 


6 6 
Moments of Trertia ES 
Maximum JI MINIMUM J x, S 
FiGURE OF CROSS-SECTION neutral axis OY| neutral axis ea 
y Recranaté. Length along ox,h; Vd! aa? < 
breadth 5, oY,6. 12 12 h 
& 
I. Square, Side =. pig A = 
72 712 h 
IT. ELLIPSE. Longer ANUS A. vit As rhb Ss 
Shorter ee 64 64 h 
IV. CiPcleé.__. Diameter A. zh* 7 8 
fx Bs aA nearly] 64 64 A 
V. Hottow Recranate.— Outside 4,8. | 1(7°%-K'D) 4(48- ke Gla 
Inside A, i si A°6 - yy (4 
VI. Hottow Saquare.— Outside h. £18) 12a) oh 
@ Tneide tig : 72 ( ) 12 C Ra Fa. 
i vt ide dams hb, ae ad 2 pps) gh(hb-Kb') 
VIT. Hotz0ow Extipse. Ps seeb es zeae z (h 6k 3b’) z (Ab Ab) re 
VIZ, Circurar RING. — Outside diam h. * ge z(k-z* 8h 
Inside ni fRO-FD REE 
TX. /sosceces Triangre; base; AS 12 
/ herghth; x, measured from Sumrmet, = ke 
XX, SYMMETRICAL ASSEMBLAGE OF REC * ; f 
TANGLES; dimensions of any one Affx, a:43 +Ehbyx? 2.24 +e-hbye 


by; distance of tts centre from OY, ; 


Ho.tow ELL/PSE 


T= BER); T-3 (R028) 


us 4@aP-1 BF) _ gp hipe By 
i E(w - KS) £242 


ly 


T =f [xt dn dry = fray ob si 


a T= Bh) xt 
= £4 feiix? 2:2x*) +€; 
3 3 : lie” 
Betwen tee Limite - 18 and +2 ; 
bea Re REE Ee LTR EEE EOD, 


67 
R) . 2b 
36 


- Le [ates % - ho 


q ¥¢ y A : Gein ge v1] RECTANGLES. 
a a ee ee aes Jo Fan anoment of anrertia vo ; 
q ‘ae a ne On» oe, as Bin. 
| x ge 2 pre Ae entre of gravity. 
| Tee Ox’ 4 OY’ mans ee “te @ ne 
Mia Geeks; 4 = Mot Meg dy = dy’ ; dng = dy’. 
= fie Ar dy = Sfes- 1x’ +x!*) dx ly 
4 = % [fare -an [fr ey + ffl ey 
4 Annee Ox = be, oY parr Mirena h Ave: ecenkre of gravity [fe ches’ =O, 
a Toes +1; abo d= ys S+ 


eo pea hxt) +a J. 2(hbyrr +2 Abr 


= ; : 
3s I Cav swing BY SHEARING OR SLIDING, 4 A po Kamgewkiol 


Atners ow sae Hane [p.22 Notes] we Ne = rr Aan con 0 
“ton Oz} .O= arekom,| 


4 i 
oe : . . sp lswn 8 + cos*8) =O .. AmMO= tor8 
q 8 
or O=45° 
r = inkenaik an due to dSrnreck (err. ure 
| Av = ot of [reraune due Xo 
P Sanding moment, 
he PF 
g 5 oie 
Ce, © 1,252 62. 
lI eq F 4.252,5 % 
Montoya re 


Lh eg co a Ee 
Tete see ape 


68 


pent : : 
§ 158 ceseat fs eek att Shas) } | | 
See ee 


Seok Sos pill nonmdeo AA jommted ake Lorh ae Fy PR PE USSF 2¢ finl, 
Pom Fark page P . fs piesa sted eet hoa: oe (5.) 


ae roe aiaheas of ALe edrvetiiwts «al Bud § ane given | 
by pa a ae ar faving heew obtoimed by soit Fe aver- 
age of ds Bes 2 ab ae bu Ato of Ah? Ber ae , 


For mpern PP rn oe A Rr ee 6,000 Y350 . 
. Aowmd - » Saibin de! Se = Se eee ee (aso) 
ron task Aron Aad seeeet eu et s, tas oma ee 80,00" Y325 


” 8.0000 3/4 (Ya25) 


Or enenar Sectusher rs) eee oe 80000 5 00 


Sou wrouo he prow — Aorted ae wtlon AK ar»... 36 ovo xe d 
- * : 4 “no. mG ot — 36 000 4/y (4eog) 
” o ro EE; Pee Ahcek: en j 36 000 Ys000 

awe Mar re abremath 2 


Bae iE scan Any hi Qoo Lb ,. Ave. res CP cates 


yg ay: = pobien Bipre eee 67,000 ow 
” reek . ssa aa Na lh a lat 67,000 . (00) 


Bo tbocs eu bind ens of os a IR hg 67,000 Y2500 


x 
tor rteel (Atvong) — poked eee pillars... 114 000 /9 00 E 
” ” ” ” neck . ” Sige ee ae 114,000 % ( Yooo) 
” ” ” Fro hows AMOR? wee 1}4,000 /itoo om 


Gon pillars ' worth hot he AUDA Rar Re above woluer ee 
7 » * eer Aoke + of Ser ofove votuer. 


ae tnd nownded R 2/z Ee 


69 


238 tte the “tewkie f qrerannne deviates frome the On? of the 
g158 Ate we mie a § 1ST , pr. 233 


3 . 
ee . . colbing ALus fi f, for derkinetiow , Wwe Aas 
1 f = (it um S). 


d 


1 a x ——= : 
1 
; hve Koh be Avy Ar. 234 } Armee 4 a” Aome aA» % ; La, PW - 
ea +4 *- 
7 P 
nr . 3 ¥ Sasa % 
Sse Eq (10) M= (Fay ee 
| Sea g Sat ato) Fee 


| ; t | c Ake wakue pee oud 

— Go “e . 

ss Pt te eee 

| es Kha o1ree Part 34 aulin lied Bay awk dye from es 

oo «Saige Ali Ares: of sie dere x’ + Ao 

a Oo one * a e mauktintced by each dy fom 
ts port of ayyieatrom,x ,*o hee plane of Aactrow x 


70 


y); 
-*%) BLO P Baha ae a OO x’ per: OLgQtwW’ __ 
z ae 
a Ce Leyond Ne 
a > . 
M=|Fdy = “S (l-%) x - we pease Aehicidigce x” ond se 
at , ” 
= “x"(1-x) ----- beyond x? 


when Moo F; Mar is where the shear 
Fag. nar Danae nayvrerentr Ae shearing foree , Fug. 2 


Fin 8 R= win) Case VI. 
Ud. « 


ars ee dict Se a She value of F is card Coan 


ee BE ao atl a be 


F, = w [%'] : tere ty ; F, = ao [Neta} Fz w (N=! _ | Ke. 


hes he? Anicessiok” wales of F committer w dereending AAA 
keow Ww = w (Me! w] Bae ma dunn M, for Aeckvow svt mre W 
Kern» BY) ae Acres and AL mh. enw Ar = ww [Not - (m-")]. 
Commow DP ference, -\ ; ; 
She formato for AW of anithanetical rrnrier ar 


$2 im'(ta (werd) . In in chee. Se pam (N-1 -M+1)av = poon(N-r), 


2N 
Jo find m WEEN as eaten m=; 


” N ” odo 5 ier ~~! ote Nt! . 


N 
-s (an the I care) ACh Bed. + w(N-i)1l = a 


fenttlas 2 ease): vaio es ae (N-1 ily ee eee 


aiterne, hans ba 1 result la makina Muay Mera 25558 
W= Nw aptead of (N- yaw, Bay peer MRSS Walaa we find Son News 


Pes wT lay Se, ee wy (LF 


7 : : z 
Fe -foode Ron wlk-e) + ore ate ... (2) 
Fox hee sate. ae thee ABE 8S o YF Ae hes Aome, 
direction , Sak cs to the right, e fave 
m7’ (C- vy? 


é PF iene 
) me 2¢ 


oo a Toubed a” gotiud? aw ire tne new B, eee anegarine 
for Mates: woluer . Replacing x ow Be ee pe Ene aquatrow 


4, —“— ww 
om oe 7 Ci ieee ee ee eee 3) 


Fax wre + 


X= C+’ 


2¢ 
| M = + w)(L~x) x ano x= eS aes M = e+ (20 ~¢ - x’) (C+x’) 
2 “3 
oM= sl (c2-X*) ites ie fads ee 


bohicl. ee Aaquokion of a parobola. 


Be i 
DIRECTION OF STRESS. 


{tow 20 = | g 108, 2q; 4) t- To 


Aon 20 = pain < ea 
a ig 
O= 45° on 135° 
@=0 90° 
2 2 
tot. O-tonwO ~ > kan’ 
8 
i ~ Aan O : 1 2 ran 8 a, 
or Aan © ae htt =-$3--& 


SAom .(3) g 108 »T.1T0 Lue bits = Tt ; ‘ae 4; An Ae mew 
quine Akr09.. Y 


Se comotanks of tegration, nai ae a portiwtar 


aon cach Le eyprerred aw term, 0 ected ak 
te she vv SiPPioke . ae poo Alan . 


Maire M a Bone 4ca® Magy 
Sor Ow wmuhorm Laded neck. wide RE M= “ter y') 
avd I= AS . z pe sioisi 

3 


ow g 168, 1.266 Ae Pave [Notes fF eg. (c) ] 
= E(mdy = £ (yt af 
Gr PANe* 909) 
ste ORS Be 


Rut Foy OL Fie: Fs ay; 


73 


= (c2_ i ea 2. Ve 2 
a os = 2 yey}? ~ V | Boe SR Se oa aie ee tS etek (¢) 


agi sib ax 


MomENnT oF .paaeal ps 


"feta sta Se 


hu = te teowrtonit Ns (age oly 2 ; ae 
abe te Z at pe | oy 


ty. —— : Exacr Solution, 
(ere : A, hi Meco Aacrnow Aohe moments aroun 
: _| le | weutral Ax AB. Here CQ= fe nd DR = eae 
‘a o 
A on a E Hen A, As + A (f+) 2 Ay 
Al ove Aaa # Aah, + fy 
i I ial 2A | 
4 & : 3 (A, + Aa) ha +A, Gather) 
2A 
a Feet Ath) _ (A-A IA +h ehdA _ B. , Are hy - BA 
ap 2A BS 2A A Pye ZA 
cs eg Pes tee eae ... Ui 
Qgoomw, L=2V+eyW . In Ain care 2) Lae 
kro , fa A: awk, As BOT ED. whence Aye AA, ECS ED + EC: 
or Awl Aas yehe . ec 2 Albis he) 
% ZA 


ans A,+A,:A 5 EC +ED: ED = joe 2 oars ee ; 
L ee ae 


1b 
quer? Mance Eas a [At eeey A, Aske fushal" 


$163 —_ AK (4,44) (A,+A2) es A Wola he) 
Su, a 2 4 At rm 4A : 
; ye AR RL ACB By) fa eae 
12 4A 
Ey VII. 
APPROXIMATE SOLvrion, ( ; g : 2. na bte| 
<= ; * Pt 2 " h, “ys 1 2A 
Pas ; = ae 4, RA, -ARA, ne KA, 
ab fea fy = a. %? 2A Pa 
ii eS 4 £08 a Ree 
jij” R= me eg ae 


Ae pena, Aon We Rowe, 4, (s- At) ook spp oa 


Se and 9 age. ae at ee 
it: paula . 1 (Ase wA(@= 899 
= (AK 4 A AME AR 
~. a (i % ee a (A,% + A, ER, +t he) pavisg) 


b) Aa’ 7 Ow mwuartsiow Az3A tas 
ee pens ! ; 

ob (ARYA RE, $1 AAR) oo. 
ANS S4 aqguakvowr (a~) and (ec) Ne eww - AWA, cancels hve - bene 
+ we 4 : Lemce ~m addame a (2) amd (6) Xo oak Qe walie 1 
Le dew - 2 ARE, Oro. cancels + ZA A wm, ; and areaterkrna Aa 
Aw, tmwre Laima ¥* agpta ke are Awall we fraue, ; 


yo & 
L= £ (Ao, As “ar = Bu arated es 


rm 
° sk A. A\A , ; 
ile et f B'(Bo 4 Ade) _ Fe a es gh A.A +3A,A, 
4. OES i ates tanga iS ata A+A, 
L A 
Buck AAA, wy EBT (Aven gSAD Aa fH (aesbADA: (oy? 
6 A,+A, +A, c es A,+ 2A, 


fe 


ed ExAct SoLtuTion L = Cent of growls of A, 
HA 


2 Piet, Pa 
A ua ’ Ge r ‘ A 
‘ aa : P= A+, 
iP : ie) = » ” ””? n” A+ At 
ibe LH - futh, ond 
“2 ne iH ne ee Sd PL ov A+A,:A, .. &, th : 
(a bt | weetrad Aris pits (%, a} 
bone oh | Pe 2(A,+A,) 
Eo; Dy Jo find Cof S, Bie A,+Az nnd Pa 
M F ; ik 7A) 
And Aah, iA, 0Q:0P , or A.+A,+A,: AAs: PQ: OG , 
- 06 = Ait ArlBa+ By +A, h,+ fa) 
2A 
Hence Mo = & Pa Cad +A (fish, )+A, (hi, + ih ay - Buk £, %. an 
“Ob = y 7 aah ae ? 
2 A 2 i 
whence Ye 2 A (Arh) As far hs dA, Pies eee (3)"* 
2 2 A 


Ss +* = AA ee We 4 + hats 
\2 


aS ZuyA moe Reteasig* 2 Fart > HG eat 


P Adie 


WG+0G =Ho- task, _ (A a Jas) 4A, (Re3 


LO =LH+Ho = & fs ahead he, “Wemibailig Raiie NEM Bat 
ZA 


A _ (Art Aa) Her +R,) - A(%, 4 Ba) 


ZA 
HO, 10,0QG me Le My? ghee OO Suinkilan kK Gk yh and 


ZuA'- A, [Garber 2 Barks (ues 1 fresh J+A(hiehd) . 567] 
& 
A (eee sah shy" ae woth oh, (os Aah ) +Aiherhs)) + 564 


+ Ay. v6" 
sZyra(= An[(&,. A.) (a+r,+A,)- 264 SPR Ad. SARs Ry(h+ ea OG" 


—- = A. [ch +2%+ Ry (AwA, +A.) — 2(+ 2h +h) (A, RY A+ As 2A +2 fh of] ) 


7A; 06* 4 A,0G" 
Now es wang 06” oe TOES ve, 
A.O {(A, bela, J+A 4 he Pe A =i 


76 
25s Blac the firrt dem vn 


,(&) A> 


163 = fa (A+ QA, & (As Fy (A+) ree 2A (fn £..)(%,+%,) | 
ap Waemee 


(QA) ree Xe marke , 3 Ae or Abe aprrotions 
gaatake Aw eq (6) , ar follows ~ ~ 
By’ a o (Par A, ihe RY(A+A,) - 2A, (fr +B, 4+ 4) 

+ A \h RY (As A,+A,) - 2A,(h+ ah +%,) (H+ %,) 

| BANE ex 2(fi,+ 2F,+%,) (f+ 4,)(A,+A,)| 
+ Be [ aad heey) 2A AeA) ye By hie Ryda APE, Pn. 
aoe bs RO MR ane aca 

Bae grt A (Bee BIE aa, Ber Bah 2 AA By 0 Bd Pace By) 


+ A (AA) (CM, 4 Aa) + Pere Beg)? 4 AA, Pie 2h, +8) 24, (A, 44.) Roky” 


+ (A, + 4.) 4, + %,)) we Pg {(h., + Ry24(h+ 4.) (h, + %,)\ + Ay (f+ Lys 2A, NOahy 
- A’. (4, + 4)" + 2A, (A,+A,) (4+ 44+ £..) are At(h, + a 


HA. Za = A, 


Cofecking anny connecting Aamer of Mtns: Avian cated Arpond ina, otters. 
WAEygA AA, (Pao hd*+ AA, B42, +h) AA Goh) - 2AM, (4.4% )(4,44,) 
We A (A+ 4) + 2Ar (4, +h) (A+ f.,.) + A* (4.4 ae ar AA, (f+ %,) 
+2 AA, (hi +h )(A,+%)) + AA, (fu, 4%)" - 207 Be By 2A Ag (K+ hy 
ang A*(h, 4h)" 2 A*(A,+ hha,» %.) + AY (4+ a A*(h+%,)* 


= AA (AL + 4)" 4 AA, (%., a g. + f,, *4 A, A, (A, + 4.9" 
Hence 


= yA’ = EA { AA, (f, + Aas 2 Ra A,A, (BiB A, A, Caan 
ae ee A Re 4 Ash + Asks 
o- = + 


S. Faa,(tae hs 2h) AA,(S,4%)"4 nA, (Ca as} (3)* 
Ey. 1X... APPROXIMATE SoLuTion, gi 4+ fas hs 
ae lee { & Gickiths Baa bah ee 
ee tile me Zs 
nae waa =] 


ay = f" A,+A2 +A3-A,+A, - fr 
ant A ies 


Tt 


Bosc oe fins the wale f ] Prom Ye ton ar p.76 swe Lech — 
: Coe ae f, AS ana regres ee ARheak hi» ee Oat 

é, bi 4; he, 4, +28, ek, j swe pe Ae markiow 
Bu he. Aertk. a 


257 nee 2. 6 6fL > 


164 P Tension, fi Wrowet. . ca.l2 { oe 
E : rag ne A. a vn sa te ioe 
: uit 4 pea a fuk Az AWG and = A 
ge a MS Yate (Aart 
tt ys Le aa ie err 
PE IAL: 
Papibasion 2 “Bee : 
A, = An. Ga-4e = a, (fc ) : ; (2.) 
z uf oc 
OLro 
Br (A, + 2A, Fay a, , 
Me fe ' * ft ) | <A (2f- ft) -- -- -< (3,) 
A,+A,. fa-f, 
$e 
Case IT. Lon As A,+A,+A, ade: te we 
Tension, f She Lact 4) 256 in Jays & ee. 
0 Pa) is My Fs 
f = _Yar46 042A, an a 
peal oli se : . Ue = : AasA. 7A, new ving e gee 
ee} | | 
; er A, = A,+A aha + Sa-Su, .... (4) 
BE MS img has ss 
aor She fant “z Aa? sai v: hee 
sith Aa (Az+hA, +4 4,) + 12 AA »{ 
A,+2A, ° 


: Buatibubineg if. aes of A pisen amo aadacing Awe get 


M, "gee Oe ANy — 2A,AS + 2A, F412 A ? 
6(A, + 2A,) 
4 Gf AA, +12 ATL + AL(2h-&) 4 2AM, (2f.-f) 
6(A, +24.) | 
9 fA (6A, +124) +A, (A+ 2A)(2f - fe ) 
6(A,+2A,) 


Mo= hf fra (f-fe) A} Ariwilarly alr = 8 em (£-2f,)% Al. @ 


ELEVATION 
= Constant 


M=Wx =i feh’ 

M,=Wf =+ sag 

" fee 

2 Tee i 2 


N 


PLAN 
A= Constant 


Constant 


. ELEVATION 


é 


ELEVATION 


261 


Tan Mic nek Noad of new team i 


To 


: 7 
: z§ 
% o8 
: pe + ok BA ee 
z§ <orppla 9229999000000 0090000eg * 
ey uM = 
ax - 
M = we (c-%)- « (c-%) ei 
Me Zeke st fe kt, Ms Weve t fbus 
Mes 8 Pc sh “id = we*_ nd 
fee, Me = =i f 0h", 


g Zz g 2 Zz a .* be ws he LR y2 2 4 
ets 4 * tiny Btet-¥) 35 ct etaxt ac ret) a c'y*, 
a L 4 ar z= 4%” —— 
ae Bt eed gz), ge ce 
hk - = Qnrurw aofe Load of farak oakcat barkcone Arreadsthe A” XR’) 
3 
g ga of pagers) of furak Cede. 


ad amo 
A, Ww’ te 


As Ww’, B’ 2 


eaten 


takvo of 2, tale Xo eal Load 


hr Vere bitdiw: ane ts Avvo iccawol ho Le vo h0-0)) 
We gore “ods Be os & es eat ee re mex Lead rach 


Annrare Aneek on Ne Lreadth (2 ee Me depreh (fh) ae he 


Aumath (£1) are man chamaed. 


We darinw Xa am Akane’ Ass acek hoa Liem AWB ro A, W’ 
2. W Snueare ee 5 Sees 4 ere a Mir Aaa we 


Nous Hew 


f- d 


Aome nakis 


Q. Baw 


aw 


me, Ao xf Wz muv ats W= AW Tye Ae = yr “ (2) 


an 


AW’ A,B 
Di honcigts Leabis: rr ei bied buy ar» a of Beye in 
A,B = 4,8. any, <= Bia. é Renee 


, 


2 st ‘ 
We 4B. - ue oe Ar Bi aw’ = A, W =~ 4.8 aw! = AW’ 
AW'-ALB A, W'= A,B’ AW'- A, B’ 
PEBRA} 
Ks OF THE 2} 
(UNIVE! 


80 


1.263 rome 253 4q(6) amd 246 VT we : ae 


$167 fm. = am We = mf bh = mF a Se me tl 

awe = uff A Ae we Soh A “, We A, W' +A, B Soe LA (7). 
B- Kwa ie. age, ee RE erent eet At (8.) 

A,B Ar kw'LA a prkew'h 9 ne Po) PS ia if pas Ae 
yt 5 SPEND amg  Gaee 7 

- 2B os eurt a 2, g 
{2,8 = wt “! a = tare * L= fete we ol (io) 
Eee : Le! :: Wea : Ze 

L: =o Lf iW BN ee 


266 DISTRIBUTION OF SHEARING STRESS /N BEAMS (ace AM, § 309) 


§ 168 : ay ae Te 5 aes arrow, Notes Av, 33 
; 5 ko thar shearing AXn1r4 £am- 
: ene eaena aie. Net arirk along “one plone 


2 ww Aknrers of ual. antense 
Ow ‘ amates. Coonquentl Ke ok ile tea 
6. prom, ar &; OW Ake verkeeal 
ak ee Gf deem Ao find Ahe imewrity 
of Une sheoninag Mr204 on he Horizontal plone whore Anane ue 
EF 


: ye ot HFD 4. paca lan. Pes ore: Aackrow wera meor GEB. Th Abe 
moment of Peckure ak WFD 4 fers from Mak at GEB, then there 5 
Pita hin corresponding ict oe poms oF ipa of bs: | 

wreck rtrers on we corres mn ports 0, planes oO, Aee- 
Aion , poe! # ar GE and HF (3a Be Care a ae aww he fires 
beak danec’. 1Xs004 ince thik ee gseerent ark GE). Shee 
difference conrkitukes a frorigonrod foree ack, om. the rotd 
HFGE; ind daa bane , wa Ahe- te’ agai Bainer of Hak 
aokid Ahe amounk of » : vires ow rte alone FE munek ae 
Pm di0104d 4 Ye onrea of Me plone FE govt He, inewsiker 
of tp. Aheaniong Atnesr.” 

det OB=%x," BE =y > BG =~, ,BD =EF (renebby) = HG (sensibly =dy 
f= aukennatay of Aroniaonte Atnss oF E. 


8 | 
1265 9 = oe 4 ee se aknors at E; 


168g, = z Ale pistons 
ie = ‘Bichnan P wee, © — j 
Z, = ” x PIS tei 3 YAS | 


Go Poms "De above aobukion Aue ge 
Saoning force AWN plane FE-z = 


yates [dpa 2 da, cannery (Cf 


— Sao 252 iar Notes 4.13 ve { Mt = By * cond 
ond dt de = May. 4 


ges Hay: iy = fit Ro pe (B) 
Srom .243, g iGo, eq, 00) JM = (Fdy } - an oe 
gas Me ; : 
ee eS ) 
Weta) Meta ay ee ee 


‘8s 2 1O* 
J Reckonghe : eis. & : fzuydy = bya b.1 8 
BS eg : 


sz)" L = pt 
a, Mire a Cini: ne ae e +. 1 zee] eS, 


(2 yay = Le 4) y dy = e (leg Pp ee bl uydey, tle general 
svkegrarl of aR fr 6358 71% rr, is ie talering BRS: Liste 
ee. Accs pwc {2 ty = 2 EAS = ht , 


x z) 


ee ois one es shies without shik mee 


ue 
VI Oe, ia Saas Se ES gi 4% = git 
[ 3 A, | . 
eee Bere Jes = . 5 frcon shy 255° § 163 ave Logit 
: A, ; {y= Bia A fi 1 J ony dg = 1(&)" (Ash y’ 
tn {1 - par F qe ‘4 Ai ag eee 
12 4A aa F = z 
BL Ar A, z 
Ce + St) 
o¢ Li eh) ae (2A +Az)” < 3kAr +4A, Aa tAs 34 Ar + hA,(A-A,)+ A, 
(AAL+3A,A,) 7AA4A) +3A,A, ~ % BRA, SAS PS ey 
= 3 4 AA, + Az 


m,-%,) “46 
% eM Me OS 
ee a= {zat 4, (hs +73.) ae 
a 3 os: F f, ‘ %, typ) 
Aukarttvrw on wer vorue (&) 156 
rae i eee a fat A ae Pes We. Ar+ 7” ¥ 
| | sy 1} 4, toe A : 3 2 anid hk 
| % A;: * A, (& paar 2A, £ y° i 
a 4, cos A ~-T 
—_ areca ales +2A 4.) A; (s A emus 
> t ,* s 


Aubaritwes or 1 its value ne &) p 
Be (Cres 00 Site eden die AG ee a 2 


Ay BF» Ax, ArA3 + AVA; + iy } 
: 2 EA 


Aeducing ARee Awe Kevvnr Awe he ees Ao MO Common deanbieig : 
remembering hot A=A,+A,+A,, and drome feriing, the 12 A torte mums 
4A af a) (F. Ars2A ty, . (&. Avs2'A, )* } 


Pe peeves: © A,+3A,A a4 


- 


33 


ft . ' pes . 

/ ; he ae pean, ropes. | Weulral Axis : ad 

ae ae < Fu INIV: | 
is i fot wake 7g. L Cy ng OF cat 


: iy ] ; * pi aatin y of Se ae aX pestipan, 
i \ 1, = Jssoa of mertia at the SS, ie Sa M=M, . 
H \ £17". or i. = ” ” ” i) ” u" ” M = Me. 
ne ane t= innkenraty of Marerr ok souk, ha as eos 
| en oi Onn bonee’ frer~ the aiepke NAA 44 m : 
Wieden. IT = pAnens ok runrhace = Wray, value, of pot 
, one Xrsectiow, 2 AG 
ge OAs 0 0. arnre ce at toto AA mode 
es ee G : 


f. Aknerrs ok 2 ace ,ak He alk Shee 10 Ms. : 
7 Dirtannee from atu teals aves Xo is .veaktal wide of the Gescs 


* oe 3 pending Came a Macspe of thes tross- Aeckion, 


ie vdelitakow) ja Jas + SOE are samt, 

a Ps AFP of i yok pom, of greateat ath a tie gs WwW. 

1 = ” ” t ‘ PA n ” » + ° ad 

v, ay’ aud Uy, ore Me values of rhe def leckion ters Ao UY awd, 
Pi ite 126,227 3149 we Lae ‘a: ott “het kh aD he 

Seo that force pout Aes af ayyplied ro a boon satel Sheekel. we Xe 
Daukle » demgth Polae tive te ax Ao goo, f kfve elarkwiry bid mot 


eo .., Fug. 2 dx (ite) dy i+ i r+ 
4 i Yea ttt we PTA = Tt. 
$ 5 . : Ants from Noker, 4.13 éq,(d), 
m. t2 Fouad 5, suk A eeeeer Aeckion, 
= ra F< oe po a es (1) 
+r Gu Eu, ey, et 
Soon Ne Combatcons miniteasas aw? ie Awvk 5% See equal 


168 phe 2 fF ee eeaare am 2 
: ~? * Gig aoe EN te 
trom “ 256 g 164 Eq (4) {hf fife £ Ye mt | 
42h « mth: (2 A} 
Yo ht A 


: , ee Se 
Fa 2% ree side bu Lei cquol we gee 
eiesrecies aie Me ode ek 
eg He Be hey 
Pa Sten DZ, Sloe . Aami =  ; Aut Armee’ 4 a> obwongs 
: v ‘nonin RR eee 
ee eer “y= i 


a -% ie ® _ 


L 


Whistle ausdokatat inn wise WO rrwrwlh ew 
md Ie at RT 


) bade. -- (9) 
li Ade Ch gp Be i pow 1s We 
dy ~ dy? tidy IPS 

dio - Mc | Oana eee (¢) 


Stens I and I; hea: and Deflection. 
Ver omy Load: ie [%- Jeerdt*: y 
ve ftdy 7 eke 


Under dod W.; Sine (2A), fr. 252 ” ‘3 jand to 
won weirs De motakiwwn of he asbicaee Lee8 ave ' wae 
: Mek. fo Mes om 


% + % sid w £03 Semel oe ene (). 


Daa 5 4M, uy) Wet 
v= Ss ft ae al 


wo) Badan’ wtvow thie Toads ane anspor vias’ ace the 
anvde 0 aes of Sars ; jad we: Melee ak 


An evident Ahak ae icieced T West phe tom. integrals 


met = an" We™ . (mt ial or 2 2man”) (6) 


. 
: ai 2 f MOL he Tyee 14, Ew eg 
“ 3 Som - » 
[ME det = a WI m'c*: = We s(n = mn or 22m’) (12), 


ce . Ma Ml 


¢ ery 
oe) harefore [Moe oy = mwC , (fa dt io mre* 
° Mos ° ° 


M,L 
Whenee 8 asus. wolusr Leconre 
La fomte (7) 
Ys a ee 
Bel Fo) ea eee ee | 
aes oak | (rs) 


Ju Aackranr of equal ahrewgth Zn Se * sh 
gg tle Se > cng cit fe Bets fyayylen 
,ts nr i a a, “as fer (7a) 


€ 


~ 8 6 ¢ 


om We Aokle avn ae. 27 rte at Mouas of wn" Lad as" canal fours from 
Bre equations 


’ ¢ 
MI. dy = wm" e* 5 f Abbe 
° M3 ane M31 


m= mm" sys ma for Riwiies Aurported at on >. 
| 
ms 2mm" 3 m= tm for Seam aupyrorked ar Loch A: 


A. Uniform CROSS-SECTION, Here ¢ 4 Noaesd Tete weleaae of 
M for cares I, TT AV, ae tin ee readihy found. 
Mo | 


27 
8169 


B. UmiFoRM STRENGTH AND UNIFORM DEPTH. 


M1 
OY a canwaktwnre 143 constant, 


C. UNIFORM STRENGTH AND UnitroRMm BREADTH, 
Here f wn tomatoe ‘ pi M= - a f = i ie Mi ie eorurkank 
_mi_ &, | 
.y Mi is At . digas AAPA athe cquakvovr» SOW eye 18,79 Norter 
ave wand «wee 4, for and £., ore rf 
X Fixed at one end Loaded at dé vhhes 


? : a 8* Bick eae $f 

me = { Ve. de =s2vevje =2e w.w=2 

m" cts if ay, xt = Ve ff (e-vFde 

Luk (Ye-t dv = -2(e-~)t hati, Yoru he ; 

when x20, ve ["e-4 Oy = 2 Ct.ctz 2e 
4 met =~ [27 (e-ut de + {20 dx 


~ £e*+20'= Fe" at m= 3 6 ™m™mM = 1 es mm" = 2 Cond wn F : 


On the above wolue of a ‘phe be Pomnd, an aaeth be shown OV ne 
by pewrem berg ALvak {Ys - [YE (e-¥) oe 

1 Mets YE (es) dy = fe. e% hee wet. 
Sime Khir Uark mothod of imbegnation in tarier me the Follorwing 


(3 


: 87 | 
on cramer mie moll phone Anat ({ 96) da = [eer x) dy where 


Pe) Ar wmekaouw oe x and the Anis ) 2 one AAAMOAL 


ALeow, 
Danone bi, portr ave Gace 
J y) +) ‘| x? 
| fsote 5 et ie. i = J plese = pile 
ik ig ede: = x’ ort ¥ 


a A feared a> mM Be Scene WAY , Nee a teres 


x! x 
he ~ (a6 xdx , LEBEAS THE RW 


‘ 1 "90x) (x/-¥) dy. , one ae +3) 
NSirron 


XI Lined at one end and uniformly tier a 


ee ee uve he. 
go> ex 


, “oy 
C= 
a I, C-% =-c Log 0 +cloae 
We oe Pere ms mm'= of . 
Saa"t* = ef ren zy (C-¥) dy = Cow mnt jnYe mom's 
° et ote 


XI or ted at both ends dead loaded tn the middle 
FS wo equal porobe Tin ons Ae wodents ORY 


found arm X&, 


“we 


AML Supported ae both ends and uni Mg) loaded 


vee Es as oe 


1 mes anreAm & bekiweert 


ame = 
he £ ee oO res) < = @€ ae.rAwm 1 vm" aE 1F708 
4, 
mie =C co e dy =0@ ue = baie back eee ~C 
ee CHE one Vom bifir . ( ) 


Me Tal = 05708, 
L 


bet ee roaay eek. g and e ot e* a(Z-1Je*-. 
IS 


278 U=zVU-V = 
oe A mere Cxe Wg! Tig ae = We > mw ee eee C4) 
- : < s ee = eee ; 
bp Resilience 3 ate why. 


SUPPORTED AT BOTH ENOS ; SUP AT eNE END F 
“ 3 
273 § 169 9,03) POR 9g o> iy 

Si Ear’ ; 


Wee Be 
mM LR aa ‘at nn 
tee fl ste oe a2 
{.2 houzowtal Arner» 
menk M, 
5 Bo 7) Akrt4 


. a Blow 
ams from Arter , n.o6 pe: x eo 

M . 
wR ie oo Sonat sates @Y 


at the sunpface rote baiting aomwenk 
vie 14,77, >t chowring the : aufines Awe — 
: shaavng Akers ar. Ae aunrfoce, 
T=2M. 
a oo pe ah eke {15 « tet + fhe Tye q*t 
et ; Bs ) Aicies t= i REE 


a ae = M+ 4M*+T* M44 4D 
ie * Vater Cops 27 gars et Fe ; os = | 
Mp 
a Y+f/hs L? : 
sf = => ~~ tVo + é _™M . = 
Th Gar te M,= Mt +/Mr4 Tt o> Be 


5 aeachea ko Mints Aton 4, ‘ge Aare ge: An paewe of 


ee for any other jie [See nde ow 2.36 Notes) 


4 


we 


89 


\ he Fiaing ae ek Fan 
Ar equivalent to mele 

seat bopper wool eo A er 
two A ar Ww WAL. mo- 
went Murr produced enweenw Bande 
AA tonrtanrt ; 4.249 ,R1b1, Care X. 


Prone 4.85, £9,(§) Notes, fi fe. fa nt, 


Bs Fano Aue conrXonk amomink , M , 5 a of the Cross—Seekion re | 


anmained the same throughout ao ake the ea eee Peer 
a aN award Hine tinathion equal Ao ue ah 


Y EZ, 


Md i 
== _ Me a i 
v= fe ("Hen Me (le Sy Aiea, Ne ag norte sarees soon ees (O), 


x Symmetrical bad ona beam of ie X- sector ,c72 
goer at o Fo Oe rok ms +. 


 aate 2H, (Wale, none cB) 


JF swe aeqmerenr ne amomemnt-+y 
3 a Tala Pecans ant et 
Oran oe X : ry 4 £ Aoe 
We Sy; bi fae ren Mo abe 
ges 


Ss Ms ithe sre om ae 
Une Wea we $ig.2, Aoc, Aa Bhd Sana lest, of the nee: 
Jk in further evident Muar any ene wtng Ken oe 
toneave to 


a quotes Routt Ow wv Se 


2... Sake oaks dei 
Q.€.D. 
VU," = ‘ Fs ee aot 5s es 


Co ” 
Trow ah) pe. 279 y§ 169, Y= sae eet rm we ct -_ 


be 28) 
134 Pt Weck "Wee mew py Aad Pre | Gt VETS 


ft- 
$176 Bre widdte of AXe de dur ko AMin Load aking watoaie 
&, G er) My 2 . ee te *.. 
tA traom 49: pte Hotes, Sy 23 [eo . Se | Be Oe par 
. My if fies 68 MM, 
mG ex { [> 2e1 ; 
BS v=," = m" Mec? _ _Mye* : But M, = mam Ms 
EI 2€I : 
« M ‘ 4 ’ 2 
— we Stet sk Ma gt at oN Mie pad pie oO ee 
Me gee ES Ein Ged) seg ene a 
She f mw equation (5) an Aerk, whould he Ff" ; Nes in: conakeons 
(7) and (8) the fm We fork 44). of rach pronks te f. 
~.285 Ex; Im 
$176 Ry aq (4), f. 248 {Mes 2 (crx) fis’ tema o| ; Buk M,=m' M, ° 
= % We = %whle = we’ 
. MeM, Diccinsin S(er-x*) =k we" Pap past + 20-11 (9) 


€x. IV Uniform atrength, urtforre 
depth, uniform load. 


&4. (1) 4.268, § 169,44 - = 


y.73 Norer ,§ 162 , {m- fl \ 


= 


/ E ‘ 
Aa) ici “ | Ney Mir aromphe Y. an tomnXonmrt 
ey! alg 1 ae Ne R 2 ; oe eS Boge ee 
is re cy eae, f 
/ N es Ww 
j Spam BB=¢ Wz ze 
fomeg jms; wes} foad 2 wee Wie  W 
2 a 
. (43), 273 8 169, ys whe} ee SE ee pps wkhe® — p ohek ee 
" »T- 8 : Em’ ; 2 SF ae Em’ h i ee (10) 
Eq. (16), pre, § 160, {M = om WEI Wet. Me ie - we - Mar tn (1) 
yn 
Mo=M.-M, .. Mz Mo-Mo = Mi-% Me = % M, 
; 2 a _3we _ swt 
omf OR = M2 kM, = 2M — Sp rr eee ee ee 2) 


Eq, (hy, p48, § 161, {M = e (ex x) f When.’ “de , Moz awe™ 


86 M, = Te Mo = 4 aw c* 
er ee Os Serr ~_hyt 3e@t *_.4%" 
Te Ms M~M, = SEY) _ geet _ [eer arrset) _ 4, eo e¥ 
2 3 ra 2 : 
wf 6h = M = a poke wn fh = oe. , mf OR M’ = w (ce sd a nf his 26 w (&-4) 
Suse” aw (c? 4x*) 30° P 


ee re ee 
a : A PM MEMS TEM, hg Pee Sard sarc ¥ =| ax) £ 


. iz kk 
Miz w MM MM 1’ mM,” q 


4 aT 7a em etc saa f rsdee®.....5 Naf [rodat ; 
7 ms [omy a8 ade? Sierae * = [mals aL eee ; 
EY at Noahs tH Coe 


} From pi. 83, 34, Note» 42% = 2. 
. Mowentk of Rexistanee = £1 dy = M 


, x 
Pl Shani 2 xe feed SE tees (8) 
el fv-% kani,) SEM xt y (adds - 2 Fe oe eee (Gd 


Migke X=l , and N,Q,&K BS PGR I JR a wales. Ake 


cbive Ly of 
mm, ww’, & from de : For x=l , veo, 2 Feed ws Me ae 
w= Ohara 
Cauakions A, 9 ee. will Aiea, Kevowke, reprectively,, 
Mo Se ee 


hind ded ee ee (B) 
Stitdani, © 4 Me K SE EU 


+ 


Eliminating F by pubtracting 4) frome(A’) ; and Mew (C’) from(B9 
fava is Em/=U (man) -2 FU; ae io ETS (tami/- tami, =§MI%LQL-EFU..... ; 


M2 + tI ltoni, =-MU4iNU-K..._.--. ..--.-------(D) 


éIbtawi/ +3 ET L tani, =-4Ml'44QL_K SP aes 


32 


past I~ equations (D) and(E) 4, @, &k acprerentrng Sre arterior 
$118 forces Ane , arene Ak RS Wher Aon 1, » tanty , me mukrnorew, 
Rrere equations ,(D) and (E), rhow dat Mo and tani? ore linear 
fumetvows of M, and tani, ; whotewe We dotuibukionw of the : 
sxksivial, forces many ta 


Load ureformly aAistributed , ar is woralby er camer 


—— 


me tax ; on = [mde = wr’ ; [ow af aen” 5 
ond snaking val, 
N= dal" ; =twl ; Ketwtl', 
Subokituting rere values me 49. (D)and(E) and reducing 
Mi =-2M,- SET domi, 4 wl ---. ---------..(DI 
tamiy=-theni, 4 oom +h WP -----..-----(E) 


oy 4 

She Mowenk of Rasustonce , and Sloe , ar Arupyrork ave Vee 
wmnekions “> th. Ahope ak the hiuteae whore the beam uw 
A ead nek te be. fined ane comrequently Ale wien’ as Be, 


Be 4 ea(0) ‘ , 
From amalaga te eg(0 M2 - 2M, ~ SETA gg aw!T ~~ -- +2 (GD 


M =-2 My 4+ eft y +4 Prt ae 
1 i eatonk Wak 4 wit Le Sif ferent Aagmr eos tele Kast eq. 
(G) and (H) ; HPeibyang (G) by ee (H) by anae adding ; we e- 


MLeaM/ (LeU) eM t wl tal 20 12 --.---- eg 


— 


M . Me w M M, uy, M M, 7%, Mrs E 
i z i ~ 5A x. 7 x te rma z SA gs analogy Xo £q). 

(I) we ave , emember- 
mg APat M, 4220 , and M 40 BSE OC. 


neti 


2 +1) Mi +U,M, - tu l?s wl ) =0 
UM, +2(L+1)mMj+l, mM, - L (al + wl, ae ee (J) 
LM, +2(Usl,) Me + LM, - t(eu,b + gl, Jao 
LiMi+2(lL+bJMn =e Veale) = 0 


a3 


4 (Beroucks 19.054 i: ae : | is 


oy ps 83,8 Notes 
i78 a ie : a ie “Mz ELH 
+ & x S Me sil 
Sposa s Bom 5 [PE a fm ft fete ot 
| M = 2 ae M,- TM. 6 wg oe et Same ee (2,) 


R a aie hes woe ee eee 
een vet) M > =M, - Flam, go ae he = ace, sry he penioye. we eee 
‘ Vi=zo = TL-Fa.+ Mm, +V, Be: Anis Fa,— Mew ~ Vi 
aoe Male oe Ma oe oo Ao ae 
(%, a A 4 tt a ( ) 
Tn Ma ey — Mag tht Met nnn ceene ofA) 
/ s < 


om M, (4° Me q,U- mM, eC. m,U iy oe | 8 qt - M, ai + 
m, 4, + ™, qab = oF Sa 6 ees ® i antes oS ARS ere eS 


Cross- section uniform arid puters equidistant, 
We (Sar whe Aah be Ow t- 289 ave Minus 
jM = M - Mt waite. Me “2(e% 7) for the Ree Ajaded ake 
M= wtw(er_p*) fer Ade Peowil Ahoadad Anon 
: &4 @) p., $3 Notes jie) ; ta) Nokes 4 Bu §2 2 zt 


Saat des Ot Rode: 
p Serie 2] 


. Pee a2 SRS ie: rhope 4 2 ford ; ( or Value ree text) , 


D4 . 
ar (MK, din Gees’ astiate avery Aiwonw PS A Pees A Gohl, an coe Dae 
oe, addikk motes on wu. 96.) 


Mazo, Cont. Flex, 
=O; Cont, Flex. 


Zso 
leo 


0}; Gntrary Blexure 


mb, Contrary Flexure 


m 


iA 
ws 

Se Oa prorikrve Dain Bhi ie. LA» norkrve Y anns 
Ave Lave iz- oi eae 4 dx a teak: » ee ra a woluer, Deflection 


v at any pornt”, yet AMe tahhe on 4.290 | ie” tainted of imkegna- 
tquations (3) amd (9), come Las mokineg {v0 ) veo} suena kobhe, 
Central Deflection under Proof Load, 
if {M. >mM,} fq, (2A) mp. 252 | M,= a “4 Moe i. wte*, 


eS wtew’) aah et 


4 ? , . 
Y= (w+ 30!) sagy ue itt, we - “~~ =< --- - (Fay 

of fm, > Mt, fond Yea wot of ze from m= £1, = rae et 
wah sia iyo fiainteel hd a 


Points of 70 curvature, 4. Ai _ My “ Mae ; 
Tee ee 


Sl and rpnan wrx work Se Reocaee Waist’ nips pharken tinea 
CF yond yap ADve qrownk F Soer mot axriot , ied Le Aw anne 
art. Se shorken tha. ce Ae oar Xo qv daree Ave in 
mowent M, before ALe pee af ASue ridge Pree < he naanad fron 
Se abutment, (see tert) 


Seis vs wall on weiead a 
wrk. 40 henaentar . Wack CG 2 
4 he Le ae rhe ate ae 
ANe- ADree forces roll be ww equil’— 
bri 

Simee CQ=FQ , Aan CAF = 2toni 


q 95 i 
1.292 H= Wirtaw ACE = Wettomt ; ReVH7ewt__-__ ___ - --42) 


bI79 Longitudinal Component of Lead 2 ED =-Wrmi ecaet Cort pant 5 
; -80.< _ Weoare, 

a ” ”  Premwne ak B= BD Heart = por (3) 
a yy. ” ” ” ” A=AD =AE+ED . 
= DB+ED = Heori+Wamri = W(la+ omit); 

es 
Jranrver2e compe. of Cbs. Wescs i haee eon't ; Rees itat ed 8 ae -) 
ge | - Weert gf hae 
. Penal AAS. aww i, + Am 1 vate a Sp 


ifs ier peg etre Ver MAL at ony 5 at ll avidenthy 
etgad oe of the weight Shawn ae De foug. th a of 
“pA = Heart + wy cost At “es eg eS MIN tort Ant) ee 7 (5) 
Ok Abe point A, ret: rrr eet rt a a es 


43 Rees 
gn We fine ne 3 LAwn) = = (sam + Aw ) 


A 2A Anwar 
" Mwh By + atte Wheont aw 
t= = ca Sao eq -(8) #185 8176 , M,= 5 Wert atts Whe ; tts 
“fe pep sw a Gai teint) + Wheost, wath --- -+2----(7JA) 
set = pa < eden. . wis . ; 
1 an fA pep = fe alasei a) ia ds keok see 
fl (aR Tt ane ee ----(8) 
mee 3 Aloha pes. Sas e 
Bak * Ah, om Sth = A = < f tama le, &e 


Gabbe of rabies of 4: Siege he qroent no diffientty. 


VIE q = bax 9.255) : Qin ( As real Ai Ae) : ALA, + A+ 3AAa 
pa aR Eis A) (A+AL)(Z A+ Aa) 
: 2A 
ey A, (A,+4A,) 
Vo CGA) (APA) 
lag a Be + ArAs on +H Ay es ALA +A, +A At3A,A,+3A,A, FIZ A hy 
4 Atay, A r fr pee ry a 

gz ALA faisohs) +12A,As Be I ae 
T= 6 (ae aA )(AwAae AD) beter eek 


ok Soe Bo a FR, 3 off es 0 A, =A, Az; wnstead of A, 


96 


A,(8A,+A:)+12ZAy _ (Ay 2A.) (Ans 6A,) 


295 = 
pas V 6 (A, + 2A,)(A,+2A,) 6 (A, +2A,) (Au+ 2.A,) 
Se = Ai+6A, See | (1 + LA, ) 
| TS gAe tag Ay+tA, 


ma" : 
ta (0) 278 SY! = stir § 
; Say u(ahy a, 
Def lection of AB =v’ = Meee dePlechin of C= % = FATES 


UD AR th enna cove 3 4 heet ic. sleek 
Fie vertical component of 4 = Vy ort 
aS VY coat yy i Come ; eon uf: | OE “Os. tJ. ei g eee (10) 

7.296 (13) 9.273 .§ 169 jy sate on 
SIT9A AGE) et "Eat h : 

“ 4 , : 

vet c . Pa nga Nn der ? 
Eek if aan - 


we} woluer of the ackorr guia. ww Mee ko le on na%e are token 
directly non Anes antaeler foferred Xo ‘ee amlihe Le exeention of 
ikvonrs [ree FS Ed. 18617, pn. 287,288), veeupus pace mow oeeu- — 
jh Goeobck Me citer of He"Bhaowme of fhe Hanes Homans” 
ma, © no00w FOX Due mw matter st vr abrkantiolhs anean : 
fre ; though AL minted An probably mort Aro 000 wan ons Care 
PDD” OE Ps Meee ne. 289, oe | 


The Qontinuous Girder. 
index. aula. mae Aneckthy, over 


ined nc Ete. eee ae AMM a 
oe Sis a : 
me. 283 (4)) aphies aw order Ao fawn M, 
Buk Adan: cvhibed APA Anak fence ame ge nw, 
duuffiecent ty get wodue to M: , Ae mowenk of Arcrirktonce rv= 
quired ok he wnrdd fe of amate A ; for AL arcakerrt fends 
wih Re Anavel Ring Sead O79 well xan Ae freed Load > a eee 


2% 


cote A Locbiad spt kde bunaty igen aaa | 
196 x i ae i 
according Te tareomstomnies tas fo Hod ane Apune x nonnrt Ey 
AA OW A A wine: res A” Seak ‘9 am nbou gar eel che fired Lor 
An fia be comyuared dat: Ae: Anowe Wine, loads 
=. Cale snActe, Ao spon of M who Urr» krone rhe fied 
aS a? for a girder fered Sorigontal ak ALe- eis (£4.24, 284 
§ 176 ) Mae Abels pork ohitlc®. antese owe Ave BP | doae 
ar for a gindex mere Ly Auypporbed ak’ fe any, hack, ris fiver 
[Care IV m.246 g 16s) ; Dds Biles moro commute Ah p ASS, ‘ wno- 
ment AW a disoando he prodaaeed by Ve ankwre Load, fired ame 
traveling , Ow a Aan arvcree bry aupyrorted aX Rue ake tect say 
Me boone Ale neolkt Ahe hana computed anwmenk- of 
flenwnir M, ab Me wnrtr of A: 2 bare ke ANie fined Led Ya: 
mae: 5 i wa) ; 


w= ” ” travelling Leas 
§ 176 iM. = Mo- MQ we Mp coke weet alo Wh, sa came hy 
4 on + “£* «# 
Eq; (8) .285 ,§ 116 {M,= 2b, i M, = fwew lt oe = : 
= ws’ hl? (ww) b memes eee eee (2.) 
pan 3 8 


= Jo fried Ne: deflection, erfer late chat produced by wre coral four 
ety feaw anere by amporked atrle and , ond nach trosk Nake 
ee ie Bie rwralore momenk M, . ; 
Eq. (13) 2.273 ,§ 169 fy = a ' 5 + &.@A) 7.252 ,g 162 aes 


fs Meth 5 a= wet’ . cteflection due to total toads; 


él 
38 “("M mM, (“(~ M,c* Lo 
= |\to&y =- = ees Fae eds i ae 0 M, 
y's fide f) Me Me ("fdat= rei dof leckiow —crecaaelie. 
7] ed mn! 


M, ¢* M,c* 


,Vsz V+VU AIR A Baa c. 
so 


: F ai Ze 


Go calie of mf 00 V. 


gee be 
he aie IES Salen) 


myo rhe greakerk Beniaa to pe nee Xie ae BoE? a Avwof 


S: 
lection fi = Memwh ., fl es 
oo j = ee Meee = (w+3w’) Sow fh 


98 


pase Substituting this value of + m tquation (3) 
‘5 


gi79A ve w+ Sw’ ‘ct _-[4) 
G <2 Sas @ eee rine s ( 


a EE, ohio Ae Roure’ He fackor paca aw Ye Aobte 4.2.96 XVI 


peeT PREFACE Fy. 1 
§ 180 Be a sre TRUSS B commelending % a MIE 
bee peat ry Payor’ fg. ace 
| Danae yaa BAB uw « perfectly Flonible 
| Benoa A ae Pee. OG aml ‘Drak BaB xs Dy 
~ DO e aka Anuar oy 
OO eh 


form 


of a parabola and ihc Maeapadeaane ssihleakan Or OW om 
re Asad (yr.188 ,§. 125) J im ae. nae Aad sansa ei 
: ight LP Hie whole of 02% fons 


wovenad acct paar “6 muAfkouww Ww ; 

sttald Le canta bug Sie chains, bak af Ne bridge Suan cv lesen 
Miveton 40 dthew Ae’ meee of AL avetalk of re. Bodonnekesne 
above hat of a car, whore se it taber, coll dams ta 
Bre daiw ouk of rope; but the train A> riled vite Ale eae 
nnd,» row ar it anover Ae Leark bit Me t+ 0e>9 of Le Coad 
A> aap kad by hd Ses j produeimne Aheowmg arrenr ond ov bene 


“ Now am § 4189 WwW, comer ponds Xo Me anew, due Xo rhe 


weigh of re. bridge itrelf ond of he Casi caer alte iota Care 
sn etomrkemt and , “‘w-w, Ko the avters of inkenorky due Xo Abe- 
Locome tw’, as oad jrodmemg Xevrrvow oa fl Saw A” Mrere- 
foe fod = H z f Ond Me oad sroduemng ahoaring ond 4han- 
din so the hunrrs in {lw-mr) de 

= e ~ { (armed) dx 

M= [Fx = Me + Ex ("eo unyde’ 

Sf tare war An Sefieden ey of toad a athrere Afra wee mene 
Auroras Ae Arwrr Yes Dagens char world. also aint a. AEM 
anny force pore ee bonding pdowank. An. nw rhe oper Aireckiow 


AOVW tarnw puypored above, 
Th iets mead Aurore Ale Anurr> Atmoved awe Dre Ss ope py oF 
nm wh nt 20.00 6 nell rarurk. rBie Ahaanimg and bending 3 


| 
| 
| 


99 


2.291 eed! ot ask Frater amore Arak ax Aa averted =e tave Ae 
bigo “a2 Direrrr229 rar PROBLEM AN j & 180 (weary) Sayer 


equilhrated anve and ww, to courerpond , we have Ue o> Fie 


: of § 180, 


a Care 


Strength and Stiffness of an' Arched Rib under Vertical Loads. 


4 
t 


iA O 


| 


P= we ax 
qa ig PP 's (uous) de 


H= The andekeounined forvigontal APrunk at the 
Pia te Os. oth Ale forces werk : 


the fronigontal component 


Wn PP) OL 


| 


eae 


es 


Pa(wdy = She Dotal Shear: oe ow a vertical plane at- 
2 WhieW force Caw be gst conrrder} rat Dre werki 
forees ne ht applied ALedetiovaey fouzomtal cow of Ae Dawe 


A ar a 


. x 9 correspon siaks ccna 
BI ccs Being Be nainces A ent af Chin hath Maca 
fever, Pls (wordy r aenibarids sith. Write gwe Ov pune Mk 


Are nb aHree®; whik Le 


Woe «0 ais’ at Ak aA 


wold F= (w-10,) Ay , 4r Ahe rheaung cade a vertical plarre; which 


“4 Ou See ee: Ha reveal 
Noe Saal pda winKo. eee 


Ommonents v4. F cord acting arn y omater ‘eo ANve ah, whieh 


MA Ane, neers Force , and oe SS Fain 8 5 ae Sea ee 


dinectiow of Mee ass aaa be alee Ao, or amubt 


0) from, 


Xo Ais Faw Arparate- OW Ae, BS I ie ay 4 comes brow 
ie Lik ag betas F atall. 5 


Go 


Tinie 4d <0 Ri ouk 4 
Pe ales 2 A. Moriga 


ee a Bees 


P = Aotel. vertical force iaehipke depends On Me Deiskak Bakion- of 


100 


297 he fas BHD in a3 Sey Aowe uot: he nrerinkoner of ti By or 

$180 wisrik “wold Se fox my horizontal Padi tone eer tie: cncwas ant 

2 Sila nerubtank of rere Awe ao R, sdeied. , Abe direckion heimg 
reversed, i» We nerirtanee of Ure obakincen't . We ass decomprwore 
ARES R, ar ter imko Ren recO and i, or wko Ro Pauw 6 aad 


Feos 6 ; be. fowner Kuso being We forces mmortly wed vane ee 
kerk. | 


FS wihi f5: 2 we Powe 
tano= 4g 2 Fe Side ss fl a 24 5 w= Sh; 
(ead) dy a (ut — Wb.) des 22 ee 


Fz f(s) dy = F,-[(w-wi)dy = E- [rel + [1B dy 


oe Ris F.— fudy 4 (4 ) so oes 


| a Bending moment at bas reeckvowr ,_~ ar yar An Are AWE 
Beat aseed be , weal aw Lenard koe 
ASve aeckificed ore kaom B hb nackww %& 5 and: in: whaelotiogaa 
sheawng o1ee An Feds. 
j © Me=)Fes®8 ds ak dserO-dy »« Mz (Fax i 


iets dae Bre Nae Aen ae tankloee Due hearng ote, | 
on vette planes, which Avro ees binding j 


Me M, + {Fd -M, + fF - fre (GB - Hey} dy 


segs Mel Foy et, vie - "(Mod = H(ys-y +x Me) 2-2 (3) 
‘A : hat __f é—_£___-}__ — 8” Shs oltiiablow of Cavrwatkure 
a!‘ oe ee as IST Be qrrodinrceed ww ue anche, bx Uuak park 
ee Si 


Fug. 3 phe itis tM, the ©) hema mood 
“4 Ny for Ahn ents given nw Ele kev. 


The other part of the toad | furds] 

Pern ciinpekathn debe anony nerefore he Akt | cit: wih consid 

af Wie- cutue AB »f9-3 ; he rectified wmto AB’ and at fre moints 
1,2,3 We ordamakes Ke Drow A at Ao’ Ae widaanad def lockions ak 

ANve Corres wndang poms 1,2,3 Ke of Ahe ale » we gek y Cone 
Ba ; awd 4 =2-M” rcyrerents Ne eimwakune of MSs eure of which 


+ in Ae nadine of enrroakinie™ tainS' tthe wae tion. dx. Abope. 


129% Ghee . oh Wie ace Or Be ie Neds one 
$180 i= fe 2i,- awe at oly = of HE. oly 


NEE OER ons ee (4-.) 


Im fg. det o send Ose 
Awe arts iene 
_twwe meee rotan ce ce ajank 
bis Bid Rare and bd be 


AMdiatn onsivined by 


| x lige = bs he 
* Boas tphos Ale Bog Sess ee 
he Dand C &w» tonaenk to Ave 


Ngee ee ent 
ko the iii. wt Sete ‘ou, 


Draws De pee ch Aa abe Ace 


aa ttl ables fein 
q aay oe a j eg pe Ce eoo® ; buk Ces ids 
| _ dv=rtdrwor8 ; fuk dwt be ». vatdy 
RM ie Ore ya Xs - Lien sre heen Ee a 
: Sle ea ies ee a war pau ar N pak 
SA = Waee8 + Fang = 4 ry Swlensity = ek 
pate, gio jaa = 2} i te, ae, Hides ad dees vik A> 
wruatly flor Ain 6 aw Ammokl , and F 2 eneally snot 
compos ww Behe pro the Ae FO may ¢ Aaa ps bie8. 
ee | aoe nopeegeentteee ene ee tees) 


iM Sr 5 
Fee fo) On ies 
ti Obey , OFzxtdy 


EC=4 5 FD= y+ dy 


Oc=x+u ,; (Jaa § aa 
ec= YU+v 4 fl = Yav+ + 
a ae vas ee 
iain Adve Awwo aquations . gt ceatee 3 cone V oue fig h 
(ds+ ot)” oe dun)” +(dy + + anv)” 


Fu. ry 


10% 


299 sts 2dode 4 At*= dv*+2dvdu+du'+ dny*+ 2 dryolu + ast 

§ 180 am adodk + dt*= 2 lx dw + Au? + 2d oly + obe® 

S. najecking att, du* and dv, feeanre fray Are’ A POP | Tre Sawe 
: ds dt = dy du + dy du 


oda 2 Ole das. 2.2 SE are. ee 


@ 
ee ee a 
pine Ya (14 SO JE chow 2H (14 Bde — iO dp wenn none (7) 
mn f{ H(i Ma AGE de = 2-2 eee (8) 
Se foun mrrnekernwined.. ornstantks’ are HW, Fy Mo wand +, Ase 


f Hie arched wh is Fixed at ther onda Ahan i,-0 ; ond af it 
~, mot fioved at the ends then M,zo which reduces ire wwm- 


from aquvakvows M,= 0,0 o gwen 4 Aan See Bek — 
V=O 12. 
i,z0,0t Mazo --..-. .o ee (Ce 


Where vu, v,, 0nd i, or M, refer ko Xre nom oft pmnyork Bwhere 
X= 38 Saez rex. 

m-13 aq.(A) Notes {m= to} rs = Mm’ Pe Pe yr aa he 
Atn094 OW Ne arkevwrol Fiber dbcede woes 1 OA Swe Aen 
moment , while Afrak wihiel cee from Afue “dirneek ASriekt ir 


rai H ob an ; 
t =” a i pit Ma pees cue es one + 


te Aruek Seed Bu F lvhiek is Fain Ow F 24) rinet tome 
G, wd Wee ubiaak devriakrow of ADve | OY of Arrrrtance 
from Nie ae wwe at ony aoe. 


poikB § 100 24,(10) {L2M2 . Mertical deviation = Mose ee 
‘ eke Wee M 
Novwol deviatwn = ee awe ae eee 
7] ct uw unyt by §, 
igi , eat ae «gee w 
Ht. 213 § 169 29,03) 4 = whe } = ve oe + f Ean v 
- 4 he a + Pe 4, AO i aoe Se (15.) 
A aad 


* Sea Problem IZ pr w= aH = @ gwen quantity” a may be determined experimentally . 


103 


31 PROBLEM IT, Reb of wert, Orr StL 
Khe Aomme find [p.252, 9162] A oc bh 


fo ete tds bons 
J ee eat 5 Se fh cov taka Anclah Sack ain Avi 


; sro b lew Babee 
Az A ree8 ; L=], Are 8 Be Are O= Ge + oe 


A =A, 1+ j l= Lyle Ze eo* 33ers = --. (16) 


A, aT, ind S. ave. ote Ahe CAA Uitlecte 200 Ox 
Aubatitubing Tee olin at £4 (+) ae: Samed ae 


BSS 


_ (4A) 


ae a Mee Rares seep. A 
ens a (norr-reekion Ay and mayo pigs 
Lending awowenke M . Smee va fi dy , in alrao ADR OA 

Ahie Aupored horizontal SN 
i: SUM Cee MR eT 


fr 
drome 1.6) {= HB) we e have do = ER, 
eq-(8) | == [fH Mf) M1 My) dn} Lecomes, ae B+ 9" dn [i Hd (BA) 


Bubskikuting for t ws wodue a ae 


we (lr SH) dy [hag sf Stan 
de om 


ee bereieeh. ANve Lininks, is! aa, |, AIe 
-{% Toe te =-i,('dy = is, ee ere silat bat 


geet a itn wolue qo wh A, ue Laie: kee heeones 
as, (ey (Maat Arence we fave for AL sidae of thre, homage ml 


Cu fl+Mi) de + Laberge 3s he 
x (H+ * 1 


banc 


H , 
he 2 os heeowes qh = 


Mande pS ee © Ahre ayyrormuakiow i ae lore Ao Ppt Pe, 


Aare O= 1 Be Ai ” a 
eae es eee 
e ied to a flak sere nil with 
Le err:  heeaure su Os e 


Bese an 


anne ctr «(1044 - Seelriow , eee T Lurk 


104 


304 Gr. Phe Crt of Aemperwture pode change ie Yoo amt 
3 and Xr 1d. ehcleceas AVis sn Tabb ieks Ae Sted Sie Pore 
Lhe ade of ara m 2#q.{8A) Ahu if T 2 greolart probable 
deviakow +f Aewyprerakure from the arsuwed akandard, and 
R= edefficien of anpramrio we (aee text mn .539) Alen ALve borigontal 
Arepomrvow on conkrackiow, due to a of Aempeiakure AD 
for Ave nirtole Aw fetde = ert ‘ fot on aection eTX, 
Putkineg: iain ae eaten) y 


wan B (1+ S4) de +eTx ~ [iG dy... s ....(8A) 


PROBLEM TZ, mrernke wo Aiffionbes , re rexk. 


8180 
% 


PROBLEM IV. Farabolce Rib with Rolling Load ; the Ends fixed 
wm direction ; the Abutments tmmovable . 


P 


k 


a 
: 
Soi, aware moehul COAL ASrak of a a of marfiown Arifparess; 

Nak io fhe eoustant; b= & reeo; As Aree; and L= Lpreeo. 
Hf he ends are fired  Fije Othe tae WSs <0 ean 


ae aquation be the’ xf eit: dBase arigen ak A is 


2 


Fig.6 : 
otewe oe torre os coerce cas = we eee ees eee - B 


> ‘ ” ; j Ah eae : 
for Ave pout B a an k 5 ape » whihr 2 Cea xX “E's j we 


Ae origi zXko O sae fume Q 
(40) Spee oisay oh (Laie. eae eG: (20) 
Deas: (20, hy differentiation - = 7 (£-x) ; ers sted 
1+ 4. = 1+ eH RL yy; 
t . ag : 
Sirs TB, ) doe = {+ i j (21) 


Also (9 a of "49 de ; imteqraking thin by park> — 
Jude =uz-frdu ‘ Lek wi, ” pies Oe Awe de: 


105 


oF Aimee Vz = V, =O 


£ t= : 

$99 ctw =-{ diy. wy = - 8d ean Wes, ee 
Shin i» rimphy proportional tothe area of deflicksin, fody 
Lek w= wenrsity of nermamnent Soom 5 mee amkewra nol ’ 

. Equations (2),3)(4),(5) Become ar follows ; where (A) refers 
MES Acaloahed aii wire tts (Oe the Loaded ¢ 


Shearing Force . 
ay, (2) > ; Fe= Fa - [ode + 4 (3h os") i 
(A) F=- R-+1~ +H CEA» + t) - p(s 
Ao get (B) sahastitute for fod on 4q,(2) fred 4 ag “Sa (23) 
fi). 5 Fx F,_ anx x4 wfr-T)t +H [8k (by) 4 4] 
= F, ee 10,)% = w(x —(-r)€). 
Bending Moment . {m= {Fax} os 
a gkH x, ; 
(A.) M= Mo + Bette. Mee gr Pree fee IBS) trp es 
(BoM ake + (oe wa) wer)", 
2 


Alteration of Slone. Simee the wh in of mniforn skifhrers we 
mae eq. GA,) fi =t- a {Moe} ; hak t= 9 anc i= gow BEA, 2; 
Aubskikuting for M ike value from aq. (24) and mtegraking ; 


ate 2 Mes i cieina: cna 
(A) «= Gan EA, M3 act (55 de hs (25.) 


(B)i: Doe { Misch AE as wfx--nt}'t 
Def lection. {vare+fidy} - Aut vi20 
2 3 y* 
) ee eee ried: -(EE a8) i (26) 


@ Of. equations of conden aie neta Seer . so mnie ag 
=a} oy wrt Se = e----~--(2%) 


L 19kH 
from 2q.(25) , ~ M,- Ae -( t* 6 


106 


sce ® Sho from (8) (26) , See: by t) 


_ Me PS Ae. (he - ww.) E a, >. eer <3 


@ M20; on accoamt of mera of ROU AAS ; 


24.(8A) is {ue-H, (1+ \dy -~ fi + Hh da § when x2 k Hrs 


redmees , ree 2q.(22), do ) sc 
: “A S(oBde +B [ote = 0 


from 24 (2 \) &(26) 


a sj {| * (ee spe 
wh, = =- R(t ee a. ent mel? _ fh : Agnes writ { 
multiplying Aw eaten, wie i : 
bag 2 k oe ib 
-Y- tes no aE (14 stlhes coe enneeseelt) 


pane (28) ‘bu 2 aubtrack ve pes (21) , 


vn Len by (29) bu 3 and Aub kvack ot from (28), 
ht -(tH - 2) Z 2 we wl wel Sh sae (14 16% 


. 
wal bigly (6) by 4 and vesbtaach i fom a ie 
(RH yf eet sel ett. ant ae Mat NS 
collecting the tev» eas 
H [%k-#h - qn Pelee \= w(t Bye Fn) 
Ce ee) gh ate eas 


amt bby ing Unennayls by wand hunging Ahan we gee 
A [hs tab, geht )) = LS wl sats Bay 


Lot ae F (upitee )uzi6 5, Maw». ----nnneae (30) 
H(i+8)R = ; Spee -i5T Pan 
Hg a= \~ +uo(sor? i574 67%) } OT RP 


Mw Poly (28) Sy 3 and rubber i from (21), 


5 4 : : 
ee MM ~ ied up (4°-5") + RH : and subrtobubyneg for H 
Ary apealue, pr 4 2 
roe, 4 ms i 
Mo=- “e caer f (= ~t )+ 52 [ee w (101 sr + ory) : 
’ Ms PEP 2 8 PIS as Be. a ior’? = 157 *. Gr? 
: TE ee {47 oe 4 [ivsiowy. yh. 34) 
j Staking <a cae (B.) (24) we fade M,= M, + A, ie - +2,) ie wrt he 
from aq. (a) : & g 5 
Fle weft wordt (6 RH AP wh ae? _orty sh wt 
; = ‘. 2 z S46 12 \e ol 
: Substituting for M, and ee SES values , 
ek Qe {77s a+ joreisrtsbr® f 4, (gH oo 
M, =~ We" -=.- i (ar 30% mare ure )+4 (r1?-br )- (fim) 5 


: ough 1-8 f*/ ot gd aoe 407 151% O4® 
| Mate. ee + — (Gr*. 87% 37 = es , | gree eS See 2 f 3 
Since the rib in fired ot the ence, avd the muowmenk of meri 


in qriaker at the end> thaw any whew fre, A fol 0» thrak, 
Re aviwawiw tending wowrnk eure ot Ae: naeatgnent,, 8° ; 
mark to the Voasedend [ree § 176, pp, 283,284 ono eopecially 4.89 
— Notes 1* eheven Liner). Ny Socge 
Ura (IZA) = a(Ht S)Y we ree ; hark Awww 
DPS eb “Sag ig Aur. ate cae Aa a may. ASrerefore thre’ 
ean: vole of p, cw ati Whe abubinent on the aude of Ahve- 


Mitoaled end . Shiv value Alen 0 

; ; BS + M, * 

meq (Ht qh) 

4 Substituting For H cone M, reir walrues fro 2q.(31) ar9(33) 


SS a Sees bp )) gee Bo ah art, ac? orkisrter*)| 
peajtoae, [wes we (rot ST 4+6r N+ Taqh et eae SET ees ore } 


. We Fa) tag ; + sat) + Ww Lae lSniet eer) . Ga 4) aptre isatabr’ }}-{34, 
Gor Tea, Lot aN, denote 9 aps AKAAAAS , aT) q/ the waxirw of ALre- 
factor 4 (Ake nanan Anak q and ol muy sf tc ce Beta 


secO 


* : 
The exact formula zs T% =5 (H+ Fsin® 5 hvac) 3 see Wotes on egs.(12) and (72 A), 


n306 at A "2. 
we othe by reduemag ar above qiwes 

4 ‘ae / 4.08 tod aH) s0r%-45T HoT? (% 
owe RS (HES ig) Gag (ort ortsr)- saat” (5 4 It (35) 


- BA )ive | 3 


Ark ' 
vl 
2 3 al 6 3 Bor") 2 : mH 
r [at = S44 +127 ‘= 3o¥ oor + sae x aT ee ee (c.) 
Rs ie) hig 5 gpa eg 6 hy ose Sg Hy Se 
qh gh gh welagh KR!” Bagh &)” 18 LGqh 
: Ab za 3 1/8 4o a _7? (22 Bie, a 
o an qh G+ 84h es Grey) aN (ay, * George ateie) ‘4 (Grerqh (+6) R : 


$ (+8) % + 40k - bogh 


‘ PAT or) alk i ene = 1c med aa qhk(+s) pier sto y= " 


) 
: 7*(2oh-s0gh)~7*(48hk+ 8 Bk -bogh) +7 (36 R416 Bk 30. gh.) = 8 (14 B)k 


. hess + heh soak 1s 4 fishs eek eae ea i+8)% 
: Oh - gh” wR- 19 Gh ‘10 -15 gh 


: 2 hau . 4 + 
apoE erst * {ss a(thenel yy - pee : 
Shas wman be fackore? Mrs (7*- ar a1)(a- steel) « ° » he rook» one 


10 & ~ 154° 
Snowe .(¢) 
on Ap, Pat Wigedd +37") -(§,- %) ar —br*+h4r? 
ae 2 oy 1+ 8 
y 4 
= ** (-%46r) (62 _ 30) 2-127 4127 
Fas ail ) (see <) 14+ B 


From wihen Me Ae Afeak T=+! A”tclucer Uy, to yuo ancl Saer' mok 
Bo reduce a Murefor 4X Bess mok correoponid Ao a Mame, 5 

Y=-! lu Fable Ak mare makhemarieally torrerprond ho a man. te physi 
cally abrurd ; ano consequently Ak wale of a+ wick. Soer eovnes— 


pone Ao ao may. > 
w= #(1+B)k rege Se Co 
10k - 15h r Fa Povcceeeeteeeeeli 
Bishan we — or tension vA + 
fy yee fond F bbe Srey i 


109 


m 30 Substikutineg Me Bans poe” oF Y, 1 Mm hak thin ie (3 
. inks satroknes eae Geet ; ° al ? 


2 (4 (1+8) &)* a (4 +8) Ry? w+) R )* Pi ¥ G+e)k)? 
e aul? (oR -15qh)* doc econ e ear Me aifek wah) 


_ Aelira)h)t _ 6(¥(i48)h)® 1 3h (10(# (+ yay 5(4(1+6)R)* , 6(4 (+9) kh)” 
(146) (ioh-15qh)* lis 8)(r0K 54 yy * ive Gok 154 ll (ok - sq) EE) 
a brevity marke a(is6)R eae pur wh -1sghe mw ; 5 Nee Wis poet: 


eeswe. 


2 fem gm , 3a" if 
3qh m* nm? ™ re me 
aq he. Som 15 34h an? aq han 
=i n? io ee n* + we 


= x6 8 ee 57 ~ oe is gh) +624 (10k - sgh ) _ 12 (rok “15 gh) } 


5 
= pele SR tite nas + bh Boe) 
2 nm 
tee | : By ‘<= 7, , Menee for the mare vobwe 
ry _ we have g* 1 rf 
rf 1 5n)Sa(sen°4)* Seale ated) weceeeeeece: BT) 
Tak. AY wou preeinely amalogour , swe Find for maw, Keno ay 
N= 5a {ite (Sear a) +E eee a) ene (38) 


matron (37) rewer to commrke re ape ecw Swen —atary Gna 
deprh ard forme of tresr- sectiow Save heew fined 
vf 44,(38) ques a megakave ABinee Alake Gate Phe ne Repos 
wolare of Wt eweins j ADuwr 
pe = £(sRH 1a) - wel yee 


1 


F= 4 {a sei as ( ¥ wo (1079-45 7% OT) ) +2 wor? - sox" 


eB 3 ee 40rd 154 *4e br 
- Set wath as )t Rae eke <3 = emi e Sa (32) 


ee Ou thir , together werk M, amd H, aubatitwhds vir 2q,(26) gives as 
TPL, the depth of Ale arch, is small compared awith 
R , its os dd Antica bal fatcbion’ ; 
oo aw Cart o ; WL AS gow pe ae oe) j 
5 te FB Ate fart fock a ony mal 


110 


30 
a EP 2 Tr Ar “aes re AX dee Re Bak av Little over 4 
e $y Le : AL 
Sap | Fe negte Panag T° i oud B, Awe, 
Gat m Sas: - ~2ebte nae > eee 
g° tis f 
eR GeGgepdeom gfe G8 
, a Ww 
ah = 3a, }(38e - 4) =f 8 | “a SP ae (38A) 


From: equation (36) we r0ee hak, uw ew (1+8)+1- gf =o, 
mar. Comynertion gees a hopn,. te load eoverr a ee oil 
Mro thar Bok, thaw (+B) + 1+ Gh > Se Ne aacennau een 
MetArhr uted he Las S Covers “ges AmXknrre~ bridge’ 

ih Abad. giao ges tee 


| ied PRE, . 

WA ig Shee) in ee 

BC+ B)R > (oa) 

_M,=-M, Ste aint «yas er 
te ie 

T° Eh, ae -( 4 a +) + Ob E2222 B78) 
, I ig We nw 

= 55 (oe (225 3a. 5) 48 q* j.-ceoneg > pap enn 


LOROLL ° vide eer” A MS e bap 
Hoong poe ABE FR I if Oa a 


wa (b+ eh) + A 


-he vk ; THA) Rec 


EA, 


ine Cee ie TEE} + te. 
where “ “> te meow inkewrs we) Ao ong Bags dhe troww, and ince ¥ 
Jie Sve whos dio ars 
p= Hoag (4 es teF) FETs. PS BR pe 2 


Gia 
es 5 of Bow ANve fowmuler of Prof, ai ge pr Se’ me pats Sis 3 3 pe 
Jo Ae affects due to tange of Hemperakures [ree 4.53 9 of the tert} 


| PrRosp.em V-. 


ae 5, sf alae anyrersaon frow wtisaks eq, (29) 49 
dr aba) a. 4 6& Wale. be 


RR AL, Snel beamedweeds tea acta bus ka Ao aq, (29), Shue wale: 
of H cledlareed os See of wmdition , at weet Le found, , means 


é wought ants Aowyr foruw 2 aa (31) f MIR afoee 
“24m Ask, a EA, fA: ) = B. 


vide for slip ark jar iw’ dhe lark 
ae we hts ae? een as ga B Pe acs = Te, 


- PROBLEM VI. 
Gahe a ih simulon ko thak im problem VW tut with 


ands mot fined . aa care M = cies aud 4, 1 am wndeter- 


Care A> ee Cost An? fo 0 aie - 


(A) ae? (HEH. wos) ben 
(B) Fo f+ (CAH wade —ao[x-er)t]} | 
(A,) M= Fy + (S88, a ae 
(8. . M = Ev +(2he — ay) 2 — wy Le Grit, rity” = ase 
) om a(Ue - 0) 
A) isi, area (E oe (48 2) . 5 3) 
. ts en [08 HE F- ga 
(4. veiw ot en{tF +(e) on 
(B) ve tc oereg fry OE geen | 


Bisse cts ase ety Has fe fot aan 


112 


2309 o=- (14 OF, a5) th {ss dy - ame 


eg S Ratitnte re olan of Vv Body am A and mukegrote ge arto 
OH aE - zo} 


120 


Hf, 1th eth Ri : 
(Ses ae) + Lege 


Hudtinhy Ay i“ "EA nad ate mer 


one . + he ind wa a a ¥t 
0 IMG geal ae ath ag oo AB) aw 


Ghar werk ion! of condition V.=0 Ww pans frown (+4); wand anwltia 
ying ae , bu PAE. , we have’ 


(2) gmk EA, ¢, ~ BE wil? wrt?” WERTH ererbe. SF. se a eee (4-1.) 


— —_—— — 


24 “2 3 . 
Ond tte Bird 24. of condition, ww Meso. fa. (+2) Lu dinding hy f ques, 


(3) i seh eae He © ak i= a & he ok 


So Ahivnmarke t, from A. (46) amd(+7), omabeip hey Ae founer buy 2 
ond rublrace it from a = Van divide bu L* we fae 
fe wel wh (srr ar*) _ We t- Vg Bs 1c +98h)} = 0 «=---.--. (oe 


12 40 120 3e+* 


PuPhinby iis by 12 amd aolol 2 yo wn we * rd of F, 
awed wh (ot Sr*yar pteet + enh 16 R + a4) - vty ore (Se.) 


ary 


Grom ive N= ean Tink EN 5  [aae-+ 9 (Sr sr%ar*)] 
Placing aaah (vith, 8) Ps ERO RIE 
EN) [ay a 2 (Sr 50", 27 7)) MN eS 
aie f4.¥8) F, ut eat! “ et , rubatitube Fy H star aechctee 
WA «tot OGPEBEM J eee eel 


oat 4q,(41) qa he EA 47 oi f aired? ww wt? Heh . tng for F, awd H 


° 
ee 2% “Ze i 


, £3 (rw. pt Se ST 4 IT LEN kero seria) 
qm hea t, “5, [ae + 2(7 A oes eee vise Clee 1g. rss 


oa » sSrtisr po friear =, 
Se toe 2 ss i 
1+C +20 T's % £Gee)- 14 ) 


L340 
180 


113 


3 2 
A, = L } wel " eo hie dead REY BF ies. -taeeik, » Sepa ects (54) 


aharv/hr EA ( 14C ~ 2040) 


is ae force ak he Aoaded.245 of nih (with an hd naverred) >, 
LOW ee 41) , 

: ° { 
frome eq, 43) P= wal ode wb arr) ~ +53 : replacing H hy rky value frome 


4 . (2) 2 aE ance _ ors 5 
y ad fiaee we (ar nt ee Peay yh (58) 


aS megakwe Pnanye al >» denoted by at 


To » fer the maximnurt_e benderg 7i0772e7t C. 


| 
| 
| 
| 
\ 
i 
| 


es eq. 42) aM o= Fi4 x (SBM — 2) 5 w(x-G-r)t) 


Perec Foe aot jer} LP eae. PE tn) 
2 coe E 


z wtp + ay. SAH 
ig 
5 ey eee VE ep ar 2 ts oe ean veMmatire (1's 


Substitute BOY Pres re A et found ov X mw 44.42) wud awe fr re 
ANWOAnX, bending mowenl » 1 Per yur nag Mg + ww S&H re for cone mentee, 


2 


M’ = Rte) 5 y(OH ua (APY 2 “we tty 


=6(E- B)e afta) (T apleS)- g(rt— hh 4) 


rc = fo(0- 8) 4 (SBM an y(O fj eee) pe . 


Z 
mow fom 2948 ) F, = ai ms as ae 4 hH 


i] 
SS a LP wr lP y RHP 2 ghHP wPL weil? welP | p* 

Mm Heh eer RH EET aE, AUP RH wel Pn eh ere 

ae 2 wt P PRES 5 wrt P gsRHP Pp? 

“t tae AE See SPE Ta 

= Lf (wel awrt wrt HEH) p_ pr} 
fick from eq (55) ret + roel worl = HH = 2P , Aenee 

r 4 oe 5 ee pP* i 
M a colt? ee te ors pkey i a (57.) 


- Fe P(t-x). saa 
; YAR ae 


414 


p 311 Oats probleme IV the y ime Aartrerr Pe 8 Ae 
§ 180 
ig pa i(neM 5 Pepe Soe 


2A 
. - 2 Ca 5 i* Wir 2 - or'.2t, 
tot Feel e ter oreer) yore) ef (ere Ear) 
ur ayers Ri Liaw iw e® denbotiiates ‘i fake 40e sie 
kmpeteen= 9" 5 ence aii abou differentiate Ad hii the value of +, 
of — mavoties ae ue dévonnnant rae yh gare + 5 ie 
Anwows ee Wa manor be oO 5 Ww ‘ motiowr wr koo eo 
ov iY Jt VAXME BA towed qauen a “Done opprommotron Lo 
Bee ahiblute pininnibinn~ Aensok > 4 ae HES founol by Aone 
Jautroduerng thir value ato eq, (52) He. we fond 


4 


1 


H = raza) ot 'S)5--+-22--2- +--+ --- (52.4) 
£ e ny Hag 
B= Ellen $2, — 5 on = All B)ky — oeeeeeeee seen lM 
by addvwg and sete s*); 
‘ Saree | 
6 am REM F568 7 a i Da SUR ie + a. a wok ee ene (54 A.) 
Fe 5 | (ope 9) Say tthe Piece op 


by adda and pul eens ar” frome Ale quidmtity! Av thie Aeaskicte nee 
aT of P (ag, 58); > t . 


oe ww weet EL 
ee L (Cu 4) =, + ~z] _ El wra lore 2) oh ELS wet ot Ss Tee.(564) 


Ween — Wer G 2§ w+ (Ho +w) CY Wo 2 (woe G) 
1+@ 
wy 4" 
mz Pw) _ fs Lwthluee Sire o-oo 


z Cw + 2 (H+ YB) LL 


14¢ 


Cor. gees | were aa Bis ket neds Pringedl sak Te” eres la 
pser well ar at athe abutments »which supposition is made im 
937% Case IV of Art S74 72. nce Ale pees ArdAuee ar follows . 

Ju Din eae M at Ale Brocaw leo ; we Nits Vda” ee 
aquation of eondiiiiosws | muh. sac a az sae one’ of Ate other 
conditions. act the moment at crowar he ewbled M, 


p 3 Pee frow aq (42) 


sl 


but from 49,(48) aster Avani 


Rae as ie rr Sy 4 wre anh 


2 ee 
Pacmag Mi 6ie Aone equal ho sack other , amd 


collecting Aer , we Find 
= gael — wf (eiz +1)} = Tw w(g-244)} i gies (2x) 
Fo = wed worth +e ; aubatituke for H rby vabue, 
F, = MEE 4 we _ wel wert awl +4 wl : 
ek ae wl (g4t 2744) wahal hi thio Meecestei ate. ae af ane 
Ba ww 49,55) P= — fF =- Te (Te ae 7 ; aubotikubwneg for H&F, 
Mt walues avd reduemeg , P a seria ad 5. = = eke 2 LS 
C , p* 
Tanaonr aq. 57 WE OO for re amar. moment M’-— PRR EE sKH) 
Me we (Greet)? RE URE lee IO. Fie 5 
hw ~-8r.r4 biot” 
Whew YT=s H= 5a (or 2); ee a cash Seine cing (3.) 
Psd wl ; Re-twl, mM’ Bes ae (4) 
S mM’ ss Ww _ wy] a 
aces +H mel Se gs £ (++2)] 2 Feat hee Bi tenipe ot (5.) 
SF san Lie foes - fw zs 
Bn aban gg Wea W) offal g (ont tonne 
tt - A aler 2) a = YP. keane 
A ald ic > ws by: = as 
th, hah 7 
‘A - 
| We = Sigma Bele 
2 Faking T=1 m (§2.X.) we fave W te Rk ge) So oc Baws alas tone (8.) 
(where H, % Ne maneticeg ‘a 
Zz 


By compar mations (52x), (53%), (FFX) &(S7X) wich 
oe wv 2 of -H - ae! 


PEM an gaat anne 


ag anakvav (§2A),(F3A.), 
p (S54) (STA) we ree Ahat the father wll reduce to the former 


2 eo 


116 


. fe, Cen, 
aS 


8180 
Sng 


Jo Klis’ tee aedt nioaders of H &e, dbbacned £ 
A J oa. Je 
“aang Me aquakiete M,= 0 , auth Vveneobbawned aw (52) Ke, by manag 
= y ann 4qs(5 2.) and (52 x.) Ane SS F. Cao, ese Awe equation Le- 
come identical only tuna 


dwr FE wr 45 wr’ = —(wr"- wis); 
3 16 16 | 2 8 ) A 
Ar 5.) ae 4X Sop to 8 oS Hk so: 

s fe Gee ee? 


or, we may surete, 2r= Srtsi9r*- &F +42 = 0 = (%-1)(x-I)(*- 4) (~+VZ) (x-¥2) 
Reva whe -watse Cre only renders ALe wolnes of H Ke rdentical 
hess Fei | 3x T=t ,or Yoet7V2. 
Jf ave Amore Ade axon be AVE Oar M342 of Ale 
tev Xo $e Pinaged ar Ae Cnoww wwe find , J 
H = 1.50 5 Ai ; 


= 2. Yoaacset 44.50 we | ; 


Gh 
= s (3.375) } 


ow fr. 3412 a2 2 (5.51) . Hanee the qo, aw Drinagineg ak the crown, 

in ww ir eare about U% , , 
Perhaps the atokerk advantage an thaw On Ore ma eo 

at Me croww Bg ANeve “canit* nae Mead an 


Cor. ae Shue affects of of Aemmypreratare sow He iwhrodlacted 
mto Ate aquakuone of rrblem VI Wowital audit: leevetale ska eae 


ProsLéem VII. Zo find the e greatest def lection of an arched 


rb. 

Evidewt Ly Se areakest value of Vu murk oceunr when iso, 
Mak 0 , wwe: lee LOW of alone faving gone Unongh oll 
ity noritwe woliar barons Ber ,rmee validy. 


os Dink: lke iogliaa of me Hee iz0 , and rubastitute Afiene 
gee 4% Ae coun ALienr sotich will £e sent: ayplicobles ime 
4,(26) ; Then Fas de o, fone Le w ne A a wll ren- 
der va max . Shu e244 gover aquakionr of axktraame mini cacy 
and Amwobving + te a igh power ; enw One Srandby available 


AVE 


412 for wre . Souk yy mohking Aayrportkions ot Atety , adbetoly will Wiis 
180 chide Ve ordinary prockierl tares , at Rows Meek determined thar 
ama *av Ave parranrg Load axtancds over Ae entire Length . Warvite 
wien. Urs a mo. , T2414 wnol yi, 
Varnng ALese 2 hanes of apes ’ 24.(31) beeomes 
= AU +o) . \ 
ree B) 
Eq. (39) heeornner F, = 2 us+ wo) B 
2(1+B) 


tas. (32) See (33) Ae yaaa & M,= -M, 3 Tuer 8 
1+ 


Dinse Sinks ack ARioses of + amd x rubskituked iw 2q,(8)(26) 
ey A* (19+ We) B- aes Kf (10+ 2) B 4*o AW = B Ave P isa wt" } ey) 


A 
‘ aurea} 12 (1+B) 8 2(1+B) | 48 qa 384 384 


zy 4 Ns +4022) B . és £ (10+ 2) B i (+1) B 4* ay d 
* Tae RER | 12(1+8) 8 2048) 48 -(w- +B gen) a. 


ee A + A+ 449) B wi A” (3 4400) 6B + RY (10+ 10%) B ‘ 
qm REAL 96148) 96 (4+B) 384(4+B) 


gh a L*(15+400) B 
384 gam’h* EA, (1+ B) 
if c= 4 (ar am § 169 he) and A (12+ 10%) = W , Mew Ale above mar he 
awarkhew 


} 


wi Wer. 8 ; 


ABS El, 148 © 


— So roo 44, (52) becomes H = L(t.) . 


sk (1+¢) . 
tq. (63) becomes p,. Hwee) C . 

2 (14+C) 62) 
ie) (Cy i, = Pilw+2) ¢ 


~ 24 qt hr EA (40) 


Substituke, im 24 .(B) (44) sound acdueng mM prreeesely Ahie new 
Add OA AA MA finding the wolue’ of v ahove: 
5A" (109+ we) [ 
384 gam te EA, (+€) : 
and W= (+ 7) £ , this Leeornes 
ee We 

geStee = Sete oy a 

Now aq.(12) 4.273 ques ates Ade ecbokikuke for ne from Care V 


eS ———— 
|) 


Ve- 


Phoeing L- 26 


J 


118 


1 er 2 Ss 
pas pegs 274 "%, 0P wel, | 
R180 af te f We and I, Le hie hates Ya as aq,(62) 
Se vy Ssas C:1+0 


(4) t: 23h ahows 


> (mn. ") 


When Ale rt waht Lean Ar Ayed hc Adee kena 
Ahak rl FE Reet Seo an Die: nnkvo fe 


which in Ar Care rr £: (228-2 en 
Iz 12 v4 


4. .Wer smd oy compared aude 


Hemts tw susk a tear v, 7 
eq,(61) + pied a 


PROBLEM VIZ . 
P) Ape Ss ae Anang AA caw, beeanire abuaia Cam 
teby, eat Ae fs moment , ano I wcenrs we ov kee 
astake to bend- ww A, does mot 

pe ae a Trem a 
ae Ae and A, wecrnrs wri fonnita anda anew’ 


Pe 
An7 


ATS 


318 Theory of the Stabelety ana Pressure of Loose Larth 


183 mae widen, A> evplon BY opps ron Kathe ah < twit. Be mn2te9- 
Ams Xo dkr wry» further ALve Elinre of ros Pes 
; Rank mer method a determarnnieg Se Ahnerr ee) mace lane 
AY acs pa Ah olor ing Awe gro b livre forth, of ash hake Ore 
ee eee | 
Sagan per ogee STRESSES . 
ce Same ind, LK luid Pressure, i ae : 
of the Atn294 ow ay ar» AB, 

prow Aos pore en Pema the queprendientar Aw Be a 
qtane of the poper vs antag Shaw te Artal 
Prrr>wre on OB = 7,08 Mand £0 atpresented buy the 
| Line ae ; Ake Aotal yresrure ow OA = p0A and is 

aeprerented buy ap. ae nwsabtawe of ‘Naren Awe QR mt Aepre- 
— ent Ww Ahrechow ao amagrikade Ahe oka Atnerr ow AB. 
. i A B+ SA* 
Hi Iukensity an AB = 7 = RIT oe ty 


q oi tage Bl de AACwW From the figure ALak QR A” perpendietar to AB 


due now PAs rites 2 had, Ar Vlucd Pressure 


LT Different Hind , one tensiow Wve other tormmprrerriron, 72 = 


=-7q. 
di ENON “i ra at figsares Joos, ard enrkt tk 
v Ae resulta Akners wll he of Aig nance 
A Skbabiele Saar ae pineal 5 tare ae Msp Akok 
ie ariehe natnitle ty AtadEow moter sath 
debe? 8 Se Ose Xo AB kn hisecked 4.5 Ahre jrimipal 


Shak “ QR aN T V OB*+ OA* 2: : 
AB / OB* + OA* ~ {i aee J 
aad vel ces fe Nao= Rap. 


ese: 2 two robbers bug warhead? dive, 20s Mipre 
of a SPE ALD mete oe: MoAY Set Susciae 


120 


FLLIPSE OF STRESS. 


Sane | eo Sat haato Arvo components . 
. 
pe Teh tet 


anh! \ f.= Tgt< Th gti 
| eae 


‘ \ 
a Putlte [7% Le rrt : i 1 Se er EA 
7 ig of PV iiceis LANES gS 
ha in’ See of f te Re: tcwnak aan 
/ = itt. = OM; Ahe Aceomd pow, Seng 
equal bunk of Aff even Aeinnd, thre 
POPS 2 PRS eg: Tat and: tae of f 
od Pik Ox Ahak Ae mormal lost 
oy ks ° saake srmdle, OR neoultantt ok OM and Om, Aenrersenrs 
Korth ned wie, evaaky of ALve’ of knees oie Ales lane 
gi : Sine Rawkeinvees wle for finding De anknwrr> ov ony planes 
whew Ake prin tego Aner 22 fi and 1 ow > ae dn Ao off on 
,: ar Mie, diskarsee OM = Tit} PD ied Urs Fe © tee 
we eat ee direction , lay off MR = Pict ; few OR= An ee 
ow $37 Noter. - 

Ake: arntenkial ALD 0. were ds ive Atak PR ‘ 
ane ron different ae i tee oR’ Ze Aayrresenkt py 
wuckion «anol autenrkey of Adee: niess iow AB Sead oa ce Avene anes 
of earth AN nkvesses ene ohusoys of Abe Aawng (aad 4k ae 
grerenck confine our dis enusion to care, 

ils tous of M is , ecole Su linne ‘eecbice ey 0 eel eee 
nadiur in Tutt: land the Loews of R in a ercle which fur the 
0) ELLIPSE oF STRESS aang therefore Ke generated 4x Le 
bit taken naodtubeenn of Ne prow HK abouk “0, ccc ab eee 
sproank R about mM, the angular mokiow of re prow R (mear rect 
from the radius Om) being double Ahat of M and aw the op- 
posite direction. The oe tion from a fixed direction, 
R AL. Aame ae of mM, huk” one wag ht ancecl and 
Ade pr ay Left Landedrctation- 


318 Nan me a4 PH Soe” Set PT eas Ore Home’ ne ae 
3133 occas when MR cach atege Xo ae wr Bit 


ol he 
ee Site. Wee aC Bae arene = veaneccaue Line 
ane Ts* Te 
Stax nr =e Aw § SX Am nr 
MR 4-4, Ls 
Be Rice giop? aa elie. By 
*% Po ThE Piem Gh + prme .. = fam = Va + pom 
“pi (t-reeg) Se p(tzreeg) & & at ge wtiecegek +ee, (ONS 


When the Ulinre” o Str2r Ar qwew we ean md Le ~Lone aw 
mccke he ob lian 38 Ov SORES | Aaleneg 2 i Aaedy 

OR =7(dm*- Be) 
Qr OR as Ke Aitineaaed Oar. Airtrver Awe of OM neudede his 
Xwo tomuaate AXrerrer each of Ire ankenarkiy Il, +%,)= (r, -7) 
Aso phones are re ow whieh the qrersure’ de mort 


obliaue- Let the anna be MOY = ty" Alen 
4 ae wy = RMO 
~P ae 2 
= Fy, he Sve AWW AOR re one OVW wee: 
whe mVS. AXve obliquity ne iA | ae ere ONO Ge, 
i 3 lg puss Ler ron mor. NY , avian “04° Bee oe. 


seer Big areanr of the’ Eline Stress ; 
i. ‘ Nae Tae af Le ees aw 
Ga dslathe Aes ob lia wk, Ane: Aanine 
? St vs evident that Fave Aoke a Air - 
Homer OM = Vy (4 +f) laste Gust e Mas & 
tw and a radiur = %(44 -p) wwe Ax- 
acsibenca. canetd 3 Avie Age bus draws canes 
* ne ann’ = to differnt pomts of ne 
cireXe , wrtensaars oblhiarn ok av ps SOK | be 
nepresented ona Bnd: eb Tae eration of 
a. tbe 
4.4 


2 OW wo tevake Ara ars Sicha. be SiN canernte 


mar OR K OR’ sume we 


be ond en ee kates bu DAVE FOI 9 AD Wwe 


122 


go 319 sae Cp fied StecPanrer , 4 ee g 196 , m9 Le comrtontbey, 
i183 rove Ww mace Ww din kina ao blew eats ote 


Ont y bythe alata 


Paint PLE OF LéAST PESISTANCE . Theorem OO ALi Ore Pe es Rs 
Ee eee cael PY A ww o*~7 ave Ay nr bootig nV aku Cure 
he desktnactn lack Awke "Ans Argetewn eked rds weekwely active 
and jes zve whack Atand Ag: snake shh phir the. Je Anw 0, 
taurer anck effect, bee PET i 9 he fe pel aa: 4o Adve heas 
eee “ere “Nha balanemg ees conrmrtenk- 
Ly w BP of ALie bed ors viene 
a pela ah a forces $e: Caused Mie actiwe forces 
ra ee AN CAtare tec Ahe ackisSe forcks’ Rates Brew Labivicad — 
ge ee Seas J a nh dentann Epos ee Reank amon 


see of balancing the oY ackiver forees Q.E: a 
IL Gx gee Se zn Garth. 


She ee myo fe Ang , COM- 
Akrueted or sO .. ext, Ww 
f me og pee Abra Xo a pron of 
6 oe. Na ol When Ate relation of the 
AXr0r 724 Ay “ate Arak ADue een obriguity 


cece wphare that ee cake g ae Fae or 
a v aa ~ whine dept Lis er °. 

Se 

t 
Olro OM anid cai MQ= MP) po Nie nakio A saddle: the of 
hn (t+ 15) = h, (t.- ts) i This anident Ahat te Cannot Ses Rees Ate 


08 mor greater thaw 


OR 


Jo fuss Bre wale f of »  OR*= OP x0Q=(0T+TP)(oT-TP) = OT - TP” 
“ TP=2TQ =VOT*— OR* = OM) cor ~ corp 


Hence OP= OT+TP = OM [ eo O + -f cor*6 - oon'@ | 


OQ=0T-TQ = om( eo» 8 = of-ean™O - paahg | 


1 cammot be greater How co9 0 +¥(eorr9-eon*#) (2) 
tor 0 ~f (c0r*O - cor P) 
me cos O~ V/(cos*8-cos*9) ae pa LD a Sale = ee (2A) 


440 +7 (cor*O- cos*@) 


423 


ouyrore at ak wadiaees Xo Wicd ne 
ee Awe are AOU patacbaMaaical mr 


geey oe wall cannes = 
ow Cro 5 mame Q raat 
ALLS soph COnrne A ee ate- oh ae 
parallel to the surface OF foe tps ace 
obo way Sve cokaacnen hope re Re w= 
Aevaity > WV = = 98 Ate Fag. 6 (a). 


In order to re ane re pprersare 
and Prmrewe bo, ee SA a hea a ae 

Os ome we See? 26 iano aanper, the ‘cuore “or Menkiek! Heat 
of ae 7 ee ‘< oF A ma qanes. ak qvvesrmne ms 
produced § weight e eS Lee iabeve Mee Catton of he 
® | iad Ade cy Ah ss Corea rt ae ewes nee 
aw tue aires of a Cth. Aw. of rhs 


ms 
= 


WALL 
WALL 


ts Cor 8 


Pressure of A HASS of earth 
with an unlinivted pela7ee pizeer- 
eer ; 

Rere my peresented bs Onn elliin- 
Aord . a indk es’ of yo PON ae 
Fo ARS" ier or ited Atresoes anne, 


rch ie Ahir s es ain re 


_ 2090 ~/(c0s*O- cor") | 
tos O + 4/(e00*9 -~ con ) 


Sup tt a ai Xin of AYe qr eaNere y, gessetiedanteat i ee 2 wienrly he OX=0x 


OX! OP in ects = wyeas 6 OM(1t 229) 
4 oP OM (cor C+ y¥(cos*8- cong) 
Pe he Coo 8 + VJ (c02"6 ~ c00*p) ‘ 


| 
: wy 0028 (1trun@) ele See eee 


ee Y= 907 YOM = 90°-40MQ = 9o°-4 (rQm-@) 
(Tem « are.sin Mt ) “. We 4 (@ +180 ~ arc. rine Ome a ta Soh ae Wig Bre Ns ---~(%) 


{6-0} f= we » Ws 38° ba | 
{9=9} ty = wee rug), w= 4@e7e) 37... L324 ee 


St; Adand conn ake AXrner Pees he yee Deuba Aorta’ ame/ 
of por & 4, “ede A> frorigontal pees parableL Ao thre rauface , 


Frovigowtal Ro EES . 
fA ve > edie i ("= t —-AmeP _ Ww coo @ (1-2m@) --{10) 
HK OX Aaa g ‘14AIn@e — tor + c00*9- cog) 


= 
"Nie amnork ayrorbann ky pQueo. re) mond ft ies . Aer Gra 
Aonar tir Mreorry eanprollee ~sdebde ton’ That the forces wejpLore 
: any trreagira©ry Jane -~sectear through the rrass of earth have 
the same atrrecliore . 2. e.<9 
Aobw fereowsted 4d rege A } » Ww ‘ Pn peer AM emene 
aud triennrr.aw zr ao 0. CourloOb sur blishredt A113 NET URE 
: denrk a aeferred ho ® Retarmina Walls fer eee Ay bu Hrolverd- 
OL. Howe, Wiler AY. Y. 1886 . ‘ 


Tos 


PB: Shay squatvow (2) rihiel tne Oanevkettike warod fi elles che 
x Pinnicbot ea ee page 3 of ere Notes. Wir artriet ly 
— aceanate hier s Hehe tobiS ave Aornded uy tonbinnows jones 

¥ frome eee cred te tte ebbiow aT in ne chen Kd! Sho vse aphere 
— Om manly AO for mworrt Aolgaes } We prwakersr AACA ery DLC UAY 
whew ARE Aaevote Aartiow ar men NAAT, ; 
7 Case IZ . win 2g.) V= 2 $,+4 s, +5| 

7 So = 2 0%. + sh. ) 2, = 24 al +58 [AerBey* j Ss, = 2 6,8, + sh 


V= ~[28E,+ sh (26, Rorhe s(Horh.)*) 34 26%, + sh. \ 

= [2 £, (f+) + s (rs oe) +4%,(f,+%,) fe s(ha+ hy \: 
% (4. M+ %,) + shexk, 4 3. he +a hha +he | 
pie Rhye, eR yee a) 
or V= x[4.(F.+k,) -* (Reel + ro B.)')] cuneate: 6 


I 


q ee hocin. Re cos tribe tak bettors nin saber aon 

. . (1) becomes (5) amd (2) becomes (6). 

i “tT Sox mend sophfeskaitions sap enn bhucwonhe. acV aw erkmating Sov 
— ww exceavatiow or embankment , eomeccally An anrelimanrany work, 
Awe ieXuives freavaXdiotr avid Crtokivalevvenks : Wiler NU 1887. - 


Te 7 “ah Comanson ana Srey bow teas of 
cha — — — bee, equilib mv the earth (Fig. 1) 
ee BG before Nie evcauakvow sae fi : 
£ ef witelenk: ankh comsietenk....2itbe 

. Akohility i» gwen by eq. (3A) 
iets 5. Ges Sd ys aS hte ee Tear fBer r.320 eae o a 
is fo. Atom <. where 4 ia the. 
: #4 1-Am @ 
j Konigontal and t he werkioat Prerawne , 


zs p= ic arcee 10 the aap’ , ean of tre ratenartiy of 


UJ + 
COPETSTIOTO B 


126 


Jee aS forigonk al, [verawne Sak rou mittee eae che poft onthe 
at the qomts Cand D 

bas Asia, Ane latalene eidiede wang Le make. vee. er a Fae 
of 4 cniaveas:; detainee 4 Lin: aieenmaes hougontal Qs, 
Hares .(1A) "320 §183 ques 

29, (1A) jp eon eee 

? T  1-?mQ- E 

hn. PS ae vy, a? Norizontal ae XY, werrtieot’ ae Re Ag fo "erent Wes 

ther greatest vertieal pressure p, which 42> eonsiotenk with 

re horizontal i states iatin d ‘4 


. 


Ap hp, eee, : Strake T= 4 Se + I+ ding” and ave 


{- Aa 9" 


howe Ts = ¢ iy (eB fy = * aa Weae- for brevity Kg 1-2mg’ ’ 


1- ame 1+A.m @ 


a Bs Py pom DK w (hah) ono 4 = ate 
eo a, , ae K”) = ath’ s nate Re Listen = nA, ee 
( a 


The apshe Alan fond a ow Ale anf aide aud if tha 
dbaker’ AWOAe’ ie Ww Fag. \ AX awonko hoe mtable jGiums ww 
Me ahope of Fag. 2 ANCROALY ae (ar D) one comrequent ly Wy 
wish Ga. conscdarcal AMnceared before Sue 10 fer nuakinial 


codudad Re “7 ea 2. 
* diotamery AQ “1 Aahew = . cok o’ Zhe Or Wnvenmime 
arate: 


win digama the dikch if it abroulS Aun out ko “be Leas Man 
K cot @ nw Katker rat Se are and Ave Qianse ; 
if Wort @’ > feot@ AG = Meot¢’..-.--+-.. 2) 
1 MW cot LK cot Ag=heot@ 
vt eae 
318 L x ; 
fe| a a el ae 
ZE- LA Ng fore ee 
Pema ee a ser | hits ocjsemin Mer 


i ht ee haa 
B % = py Be dirnXtoanee £ bee Se omer 
aay gaat where a es Wee 


re Oe [te ; bak o= ae i be Yo 
2 t 4 -* a7 WERE 
. 4, 
se BP 5s eae 
- ram 5c le ie) , 


on ; 3 : M4, 
ay, he ougue 4% aki biec Centre of y jae | [sy oly 2 a 
ie pres X%ay* on ES is 
Aur of da Am, 
Dhice we have used 4, te mean ther same that the author mean» 
by 4 ave owe I 
Ses sedi, eth oye Se ee aS (A) 


ty 26 ; TS 4- Am 

ASE By (10) 319g 10s} Ts eee 

Wome bo ae motakiow of huis arkicle, Ave tule 
the east Aaorixontiab querranre, sehiceke. .00ke 
holanee Ne + mkt fang ‘Due squrakvov 


[% = doame . ty = (2 hee 


je 


wer = (me ) —_ po ( emer YP 


1+ Ame 
rie | fe team @ 
SNSE nf, 


Su the same way thot we ride 


a, ,  tquakron (1) we ger éq,(2) 


Wwe dS (1- ane \* 
T% (we By 


Cuatro (3) > only Xanre an os Wie Aa 
oy equality We ads aq, (2) Are forrzon- 
en ms =e OX Learrt Auf fh cecent, Xo Rolanee aw , 


| a “ fe = (ame “We go sae ee ae 


ee —-~ 27> — ee eer ee ewe 


T Ducking de | a 


'y Mew ~e 
. 


ot 128 

he oukad wh ar svar «2q.(i) $236 
1379 fa. § PF as Fe) 4, § ; 
| pr Wi ral oa 


x fe fq, (1) 42.163 § 106 ix, = eet | 


ATK: 
ie N U,. ka wotation of Ahad prerenk aarka he’ 
en Se 5 ee ER ot 5 a al eS fio- i 
va 3 ty P ? y) 
f Me 4 c T*o~ 1. - ie - 
we bse by spe Sa, -. Pe pA 
SS a an Te oar ae ae 
SECTION hs é = [> Ay = qh i --+-++---- ( ) 


White O Falf wan Shit A and B A, = tag 


we _ 2we mmnenicl Fas z = U-sre)” 
— = = 1+ aan \+am I--bm a 
h Seth SS roa ete Se y ie 
a 4 —-LAMg| +Amo =i ag 
Ad one 1 + Aim 
Wwe ~ (1-4m¢9) = we ee 
Te 14+ Am*e@ 1+r4m?@ 
trAwge . 
Seah ts Lm. ae Grseeg) =] _ gh Aaen of saree 
Y ts V4 wy 1+Ame@P plant fs +1 2+ 2™"*9) 14aus ¢ 
iGeteee (1- ing)? 
| % A tt ie ig 2 4m @ ee 7 Wee (7) 
4 ey 4 1+4m*¢ 
| & vi 
p38 i, Lz 
§ 239 tq, (2) 1. 319 $ 237 = (—) 
1+eme@ 
ae - _iertace 
Pe a, Saha Which iw thir ease Feces : 
pag fuia 1K a! (A= amg \? : 
1 we & Pd wx — = 
vs SF ec] Yt, + wx Gremersan & 
x ;2 
we = +h wx 
t 42 
Age Be 


SECTION 


429 


Let AD=t = ADickuners of rs a 

G = sited centre: of pressure’ 
ls a of! AC =f" = Final? of MARS . 
: AON tha: Aniamale ACE “so hat sabe 
h anca = R _ pressure por unt of breadth 
: ow ALee- centre of MARS 


AG@= AH-HG =}34- qx 


.* AE = 3AG = 4t-sqt pete. ACE = £ (a4-3qt) = e 


oe ae se R 
“f= Grrsayhe peat c<saeeeee 


oe aa echover care f= AC > AB (AB Se double the nana 4ressunre’ 

wher rhe prersure Ao dlintrrbuted over te entire bare, or equal 

te weal) ~be-the. nian’ Amnre af ak sere gere ak D) 
Buk Alene A? eign oh tie. Can uphiene’ f= AC <AB oe F’£any 


° H : Se 


OE tell 
p.379,§ ee otherwire ie 2 


fa 7 1 163 g 106 7,8 ater) 


. Ee: ae 


is 


a Ada figure wwe sae that Qa F-t. 
| we 


f= 428 4 


cco Benes te RGR =F ae 


Ma Wqar)t oj Soc ceee ol 
Wa senabbtec owe Se ae 
Mz nu (qtr) ae ie eee se eS ..(4) 


L= wreak O ~14' nan 8 


PL= P(x’e208 -4' ran 0) as Mare (5) 


OW+WE 
$263 Pom 6 +W 
re Row: are tan For 
th Pawn 9 +W 
: Pevs & : eee eee 
one tam ow pth eee SRS EES (6) 


— 


1 oe OQvv'r 2) 7 ae na (4) v4. 
mak, ¢. Cs ss ong ¢ 3 “ ) oh ” e . ¢ a 


ie PR mse wl § Ges 25 ae ~rimO) = i <i 8) 


w “Amp 


4 6) 


aabaritulrneg a A ite wolue from £a,- 6 
Ae = gt solerd) ccolesty = ten s8) aE, sc iad <a 


Aaa card 


49% 
3265 


ir 


f The Lever onm of the 
‘ pe ae 


| 
| 
ee AS MD~ND 
! es, : = bo ueeu FD Am (O44) 
\ ) aide 
i ade ‘yee GBP ena 
A \ 
Re 
P Sy 4 
aa | BT 
‘o4 ae Bis 
coef gee 
\ as “ 
; pee 5, hepa 
twos ® He Atnigomemetrical neduekiow aw tq, 4 


3266 M4 ar 2 onus IzAxes we pdagy too(Go-9) - Arua’ } (40 0-9) . Aah (IF 
pers i+ 0+ (99. \ ae Cer h, (40-~ ¢) tant ( y) 
. = 10-4 7 ; 


131 


By re ma to Case Vill a4 
“4 mu $1 
H “wey = ‘the rhe Diptonia 
a4 200° aS swhere~ 00’ « 
Mier distance of C. of $. of EQN 
C, of G. mv ste Last portion 
= (w dhe care) 4. 


2 Gga t EQN. EQN... 2-22-20. A) 


| ME Uolinse- ak wiarc mp tha es Bons wot - 
$264 f ‘es & (bt+ 5) 
4 | Dele’ of amanowny ae » Oe requivatent wmiforne wale 
x h (6+ et, = V(b +e) (6t*. 5*).£ 
Symorinng and Aasteting ewmmeons terns, se Krave” . 
2T£ = T*+t" 
Bubbracting 2Tt from both members, wes get 
) oz(t-t ¥ 
Simee T-t tan never equal gene 2 Metand po OES FS 


z=) Hhe- expression Mo ohusanys gucter- thaw Aha’ frente ; or 
amnounk of waren sav the cowrterhorted ivall iv 


wertreally, ALDAMAL’ O 
the i. Mita ane f 


132 


1+ dong | 
$272 vee « Of brn moan. gu ll ; however, a part = 
Js aa ge Peis Wee and haa: One 
mot Gta Or set Pilea aaa an sai : 
Gt snabace’ ee Dob | ee Fiokizontah pull 
Wwe . 


[tssend _ A-Aine 


1-2m@ 1towg@ 


= Wy damn = ert ate. 
4-Awe 
x, : . 3 ae 
H- , 4am a 4 4. dan bs 1% i + mp y 
= is tos * 9 Ee tos" 9 Late 2 ¢eos*p U) 
priz She- yrerourt Ons Adve pouticle ae 
q27% A : = no w2~e- MG and , ar AVRASWNE 42 Lue 


= ato ? AOWY Wy Steiger pont a”. Ov Langer 
oneal Bi plone; ALe 


I 
er 
g 
§ 


VRP Aone fore ay the one at G [ moke 
N Awe! cae ; &L 
\ EN @ ; . MG. w cerP = cory. ar we 2A 
N Woe Qh : merkical 1 bear ental ak G | 


OS re Resolve thin pressure’ and tees 

Frorisoutal davon’ = MG.w eor’@ 

ie wette wees Rak  baldiass te horizontal Be ei 
p A- Am 

A+4m @ 


Co rrag Eo NM+ mH = £7, £”, AVE OS : 
MG = Chong ay An Han p. 10 cos'p = wy tome 


+ L"_ ¥eot@p 1-Aam@ i ND ene a deateate 
Con*P = 14+Ame (1+ dim @ )* 


Maliteh abe.  UReRO NS ut 155) eee (A) 
t © PL + Cage 


= wy. 


133 


C8 = le EEE) § tat ter pete. 
Ree satincg Pk tacky hs Pl as a 
So pe ert ee 


te 


as Pp’... PS WAX BOY LY In timng 
4 2 ee] 1+ img 


8 pet 
see 

+ 

* 


«Sh aatnabon 2 the 
Jrzanstko Cake meed mot 
e mo dice ae ve macy 
he dmotnan Rudin Cie cakena- 
oo @ 

So urkrote . Supprare the 
use ae of the soegarc Bekivcen: CAB and MY =w 
Sen anes 7) vert sane’ at anky, ar G 
of CAB = ay iy 2 oS EoRig) ouibsel Due Ree 

3 Se inant’. touldr be Cis fe w G hug ae Legs 

bank 6 aX Lok ao wat, weight “of Aha’ Peuccn waste 
= ww’, and Let r'=3 Ww ; Auew a column of the havin mar 
Mewuat iv tose rg hk = Ea iathastd que the’ rome prerranre ar 
kd lowe’ of Us Miho, v, 
Ok taal. pomt of CAB Bote aren 5.9 Ae pita 
Bemate aud Hecorwah Ahere sos Anraw curve CAB’, 

as aye ree of Afe Aoad ‘rea? Rave ys ae Sone aud 
CAB sk fh he b. Pers, ander the forces. 

Gee Aha ag uakvon of CAB %X% 
4 = ie (ee at) iat of C’AR’ 2 ew dently 


Tay bax added Anak PoC 


134 
y= 2 (e™4 £7) 
ee wrote of this exam rte in general. 
age a op pis artradsor be Wig ith ee 3 Catenary. AAI CY 
mut note Mak , POE a 5 A Pe Sag 3434 a eat 
covrespondn Ae Ga OF bite a apoee’ ehoeen CAB 
? ie, 2 Fi i sees Saal ; 
Be a a> the aoa ht 2 a ane of vol. of Ful mg, material 
ek ae J Meare Bae nib “pb toda Raw, ; Lohere AAI, 
weeght of a amet vol. of ther budlSang matiriol and 


ir the 
ew Ag =uU Wns = wt = = Se (2) 
$419 x at ee 
cee C4 12 211 awd 3 
233 2 ° = oe a 
g ete 4. te jx a ges f fy tpt 
2(%,+a) , oo 
A . . a - a 
Substituting for xX, ak» walue’ fo = oo ry a 1 oe 
Oke ep aaa oy peamermes hg ee ar 
age 8 oT Me eae 
Sindarky Ave aletacan: @, = 2 (14%) 
fi +20 (x, Pit ‘ j ele’ Sear gerne tes ics +1) 
§ 234 a bi ae 
ot 5 
4 - al x ) 
{8 - ¥ +.) | bq.11 pee S «mee £ and 4, me nearly Ade 
Adan, And vince is ~ only AOA xamake- omula any 
pany ae NE 


SS % =7 Ty «eC tq AL213 137 where +4 we. hee 
A i M% ; F 
| weedeat) of Ade horigowtal pen aares ano Ns of the wertieal 


ME ttt Re nividuibece eak av ane prerounre— 


139° 


j * eT Trorizontad kev Xs 7 Payor anny Ave Aunfoee Leek 


gee ~ Ts aye e 


+ setae Ae. 226 ink Ave Vqputal ce ment of the 
ARawak of Ahe TOUS 'R V0 P) ‘aoe A” woaX hover ther akeae 
aut. . Z Spice i aie Ntorow we Jrawe’ Canin ebro te Catitis ov 
mM hoorma, A wm Equation’ 4 a : 
Bay nchew Xo tar. 1k 2 hse 
ans Sf thede Noten 
are 


k ee POS) be. Raw ore 
Surface |G oom 5 : 
es : 
2 A 
eee IA 
D mat 
oe 
= a 
B T= Q, 
Yf oi @4(New CENTRE 
rs 
fig nar Ar enawne A’ 


Componenk f oS aR & H. : 
mad the correrponding dhagraw of forces tah Peg. 2, Na 
ends « 

Whe MAng Auianiim ok De Crown 14 ewe J apepretie: ; 
Ooww A> Ford fy droavond AL tuk Ko thek cua hurr, 
Som Lig. 7 rome the “pom w 2a vertreal A the eof. 
hate Tukersects DT draw a horizontal fine, this interre 


. 


Bre OA at A’, the mew town. Other he 
: abe pes 


Gan 6 the duaandws 3 o1ces Aron a 
Spo i aes ee Coa 4 os Pies 


Bre Chagrowe A reer AVY Caw Sue’ ~rhaapro- Ae ‘new 


136 


tt Abe eortre of Ae aie atoaas lau: the aack ppeen Lav 
§285 stable Pik fale within the wmidSter tind 
Cont re 


Vv U a : ees ‘ ‘ 
1423 Ps wor | (1m) AM t = — i il} 
§ 286 9 ere qr. 58 Notes 
r) Ahn anno Seana Ue ayy here 
A mise. mat, 5 ws ww’ 3 Te x 


Spon has pa Beh Extrader om, 
Ps w'r'* (1+ fr) Pant i ogee i} 
Weight of arch aang ACFO =w cre 
K “8 Gon. otal Noas 


x y : - ues hrs 
P. wir! G+ § ee. pan weeny — 4 \+w FZ 4 
Hy is ot Fo) Afve ADrrnk H= Pott = P gost 
‘Hs eet [rr f {+ $,) oan i ea ee — i] x 
He w'r' “f (+8) (ort sm aeate 4 acts } + Ww Tr cot 1 
1. = ag : x he y . 
H,= wt fos €,) Coot, con - fee Sed + wo TA, est 4 (2) 
oH i dit 
138 Lit a= = de 2= <a 
ts fe ) p, ttt wet tye- a & 
2 4.° ‘ . 2 . 
Pe a A 3 ‘ cant 4 cote _ wlan) ab 4 cote 
Ty Vent Z fore eis ea 2 Plant da Bote 
buk\ 2 Bs = spine v cpio 4 psaht: ae 


é,caty , ‘ 
dl ( = =¢% cots, de t;- 4 Jolin = 4 Stivconi- te 


is t4= -<o f(1+ £, )(- au ae mea ore ) — (~teamatreore teawnncere Jf 


Beet os rey 4 
_ wl ~4") A~ rn’ — 
Pl aw t 24m74 
w'r’ ree imrvrt-cost) . w(ri-r) 4-4m4-40n0 
y= j (1+ $.) meee: OE eng $e a, Zoom 
De 4 = 0 » multiphy ing by ” te agen 


Os wr’ {(i+ = Cort - ig= own th c00 ty | ual at), & ~ a Se 


ig 2 f. a 
Ao . - Amt, 4004 Le ~ Amt, Cot Sows 2 
4 Be 2} cost ° oly Bie ore ; Sp idee fam 4, c%%, 
Zam? 2 Am? 4, 


O, ; 
Vv _ fe aponrdil FVUP “s& composed of tivo 
v | fs Ghe v0 ckangle MVUP 
s ind ” surfaces FMP 
R ete FT = OT oe PT=+ PO-TO =v’ (1-4F } 
cope 2s eo Henee One of sector OF P 
4 ~ = . . 20 -E =.3927 
; S48 he a 
Onea of Aviamale, OFT (ve) = 0-25 7 
¥¢ Seganent FTP - 0.1427 7" 
yy fo) 
Orta rectangle FMPTs PTX FT = o.2011¥ 
-. Orso FMP = 9.064% 7° 
F me > 
Oger MP =FT = rye , Qnta MVUP =CT $ = O.107!1 Cr 


Obse = of wma FCPA =4(tu'- a7") = 0.3927 a: ae, 
Ce Ade hele maccght ACEVU- areca meanhy pe 
36 ae f “y 
H. weany = moe (0-064-4 "4 O-JoT! c) + 03927 ws (Y= 7") me. (4-) 


Bre amet © fon bike. 
wn tLe divtomce marked @ . 
2 ew Ci 4 

N= VataB* . 4 
ees Se 


Pee 2 ager memes 920 


e 


-_ 
oe 


138 


ee Surfice , 7 
$297 ART LETTRTTTETOET— Sanath of Summed consiclered = 4 Ft. 


3 . Shs? Wet ole aaah Be 
Bs , pugprorbed ok CF = weight ABFCB 
| 


= ABCo ~ EFO 
= wx (B+ t) 4 ob ws 


= wx, ($+ +t) - aoe 
. ge rim OPE = st BD _. (a 


sea eee Setiaasi ie 


St Sa 


dha of Spal De and a 


f-467 q°= 


§336 80 ; K ‘n {Mam = mp bh” } {ae 
ak 


Ms 6 Peace ; ; f 4000 Me te 


LiLid he 


Tce wow Ab otken oll: dimenewen. ae 
i athena Np alse TaGI a ill SED be lone 


ected ffs mw} 


h i 2 
: ee 1eee bh 4 w. 4% < wt) 
ES ERT, “EET Po Fp“ 
2 | 2 2 
| | | | 
Ww Ww w ; 
2 1 Z 3 


Ww 
z 


Heo 
Teo Mo PRIMARY 
7 ~ 
deo Xo Secanoary 
. . W 8B 

rg : 2 o 

sy ~ ; 

4 10 ! T z ~ 
7° 
¢ 


3 ro 7 2° 2 


Tee loaS will be dintibuled a» rhowm ww the figuee 4W 
ee at each qe of Ahe nafters ave ia W reeling eae 
Lertir: Tritss 3s ra vornrt> ea ES ar ints of - yy 
for We W shiek staty at a and prance ANe pats 3 Fare 

EW ne ; ar ; ad 2 
the rs WwW se directly 6 amatrang AL 


Gurr 367 mW+twid W2ZW 


go tat the total “amount Arell upp by the rol If x» 
gM = 5W add tir to the bad resting directly at 1 
fave SW+ EW =aqw on Ahe fad on 2 primary Gunes 


ae att $e ahaeies Aheat fe we Aupprorse Ae Load form 
eetitatcdr the Load on cach tus 1 = of Ahe rote ba 
directhy above Afak bruivrs . 


ini mavens Aniongtes H pease SR - Hs aE K t= fH ¥* 
OO ANve diagnawe of Forces of ANe Aceowdary ' buses 
Kean tb 
ree e CB =oH(Aawt + teow ') .. OH=z cs 


BH = OH Re bic d 4 eee 
- HH’ d of We 
5 6k SR OR ERY ek 

on S 


u : : Wi 
6 
$ HW. Be; T's 8!2/t™ Be Ao eee. GD 
1 We . ee We ue We Ww 
Heda Be ot A eG Han ME £98 Cb) 
re 
Se 
B ° 
H 7 
SG 
¢C S< 
FE aS 
A Ps 
cs q mM —& PO noe RA 
Ceneral Case 
the amouwt of Load rupported ak wack yout 
So fund he tbtal Load to ba Aupryrorted buy Anurs 
and A. Ghe load ree “oe F will 


“ye 4 

Po. Laad = Pull on et od 5 wre 

Re REL RM FU a SERS gE 
en eb 4 9 22> aa 
2S » *s = ante Wes ae 3 FEE et at = 4 ae oe 
ee le AN rr Aw 


+2 
2 a 

(|, er we see the daw amc cow write the Load for 

arn the Annes ACE, Goin toad Kune wut te : ey 
hotweew A and C ow the one ride amd 4 of that hetwaenr C anol 
R on the other. 


ARE OR Pe of nettaawn nw AC un (god i Che weg ht ak 


B72 C = ——— : Avinitarty Ave get Adve wag ht K= twa 


$339 tnuoe ko he ™m-1)4i W LW the portions of- ris Amyported 


Se ey eR 

Ay ha eevtial rod BD ds 2“! Ws (mt) FE. Sines aw Canal 
pwm0unt tomes From Nae other AA ey Kuss swe 4rave 
eG otal dead Asstima ow the rok BO : Ww: 
et et ah Bh watinvaats cde fe Ps 
the Louol. nesting Aire Bre ope. gees 2.1! Wp WV = (m-141) 
wr the Load om the puinnary ture = 
Tf ci the mth joint wows tthe eoutie thew ther Load am 


d 
Yow above vo Yomet! WM” OGL un the tnian gfe of Lor 
Be, 48, Arr . a. ‘the hie: snbatt brvanahe- earn: 


ten to ACM aud Jos ONL AD OME 
Henee CM: GH:: AM :oH 
and CM: ME :: HL: 0H 
w NWeneg GH.AM = ME.HL 
ond GH:HL =: MEZtAM $:@R:AC fh tf we 
GY: GWYAL i IS m= et 
Pe ere m-mtl yy W 
: Gu ee ae tes weet ae sian 8 
ines Gl < weight ak C 2 Somes! w) : 


OH =Hmw =, ¢ whieh x2 medetendent’ of me and. comrtant, 


Aw K 
s—2 Zz % as : Zz Dy ; 
ene FT OE 4 OE a Rh ys, He MRSS ey Le 


HL= GL-GH = 2 GL soma SSH we ee Ww 
Seed on = OR = fe BE eo = ofa od LT) 
Iv B o 
- slo “Que Diciaieca (iia Ate: Besek Fig, 212 
o fiat ae “rieces whieh stout 
Dv D : £ ‘ 
\ be heft awk aan the dis tuassc0n 
Zoo / \Nale Oe Ane boaS strortS Be conriderved 
8 / ¢ g B inti buted ak Hwee a0 many 
/, ‘ Al re ony yoeees wren 
Gothic Roof -Lrusses BC Rankine considers av aching 
ae telae ia a AXe aceo : drawueg t 


She duagrans of forwes for Ae Caer Anas ADUA’ ws tonviues 
Xed buy drawing Ga'=3w the Aokak hood ; from G Freee a Cs Chaw 


142 


pee Hover paiatte! Xa DA and DA’ wqeekind anv .0. J hewn pneeeee 
$339 neresent the horizontal Abinet wm” the mice DD’ and OG 
font the obfaue thwurt inthe direrection of Ahe dotted fine 
DAL Drane OK || BOI] Ac - Atew K wll Be Ane wwiddbe 
J he trtang ve of forces oGK Gases Ahe forces 


pout of H G 
aching at D om the Loe {reeds 
GK = 2 Ww = Miinat ow DC 


OK = eee aw BD 
a cuamote KOH Aepresents Ae forces at C and alsa we B 
the Ww nesting direct by at) Bick. aoldled 


— 


vefare 
OH = enrc08%” mv BC 
OK =~ Ahuwt OVE AC 
KH+ Y= tet on BA 
OL ar Ake Aaguwe of forees for the Anurs DED’ where 
SS Me =¥ = Kotak ao OVE tS eee Ain’ 
~ HL=%HK «. OH=%0H avd OL =%0K 
OW < Atencio aw OD ste Mrerof-ore equal marmrericodlg 
ko of rowed ar Comyudsrson as Pick Comnts from Ak» bema 


AL miwbher of ALe qrmany aoe 


M= HL 
{g 162 ws M= wf bho - ~f0Rrt 
_ 6M ; ’ 6m a) 5 _ 6M BL pet NN eee 
Js ee De ee b= pt FR ( fg = F--A%2, 
yp Wwe Zoe Zlnegruedl Transversety a 
$344 ; Wz, = 2 (a4.z, + azz) ie 
We,x2a(ste2) - as pen 


$}$ Zo Ze 
B Ww E: + tte) | 


a 
3 
ie) 
= 
| 
! 
® 
N 
Pp 
+ 
N 
~ 


Ss. 
. 


Nahe Loa8on D=0 =)_20Z 
“f 2(z7+2}) 


Lo . 
3 Z,+7Z, r Ase 4 wa z= raft 2 apie ~—$- S e e  = i 


Sohal 


443 


’ 47 ae Toad Unegual Longitudinally : 

8541 Ma Br +e - ae #y.1 Ber the truss 
in “ he Ia LEOAS prerks at D the frome 

: oy, ee few Ww prorkrow FOES PS 

buy OW apy ad Force = Wace’ +g at 

Do oe a ddimuaaAe force = eekimg 

Fu. 2 t ake C $e ar PS AR EG Sik Lig.2 , by 


% nn ad fore act ak OD 
; va PS: =| : SNe pee pony, acting 
SS at C= y 2 
; Su Fu 3 Are uk LoaS v4 Koime’ 
Boi a oti bani Wren La Cage 
% Lowe 


dintorted we towmrequence’, Ye 


Ow A when meee 


pom Ko Come doaorw | Aumudtameourty 
the jot 4 008 Mfr , Cauamag an 
spatiand peal ow » beauy at 6G, 
Tate the bendang A me froportaon 
hs the hoak aed” Sass + aust gu 4 


ea 2 v 
WY , 422 1 Conners CAorw , Ahe apuarcl 
3 mt ee apurhios Ao the Beaw ak 6 mut 
> Ne eo Ahe Aamet’ «ar Ahe” oumiiiicks force 


ed at 5. 


AHD , sohite s moment of the dowward for LW actan 4 
: as nomrerented buy ALB of f 
: q é | 


Ce ACCORD.) 10 Atte wnantewne”. ot Ake 
oC 
5 at athean 2 which At v7 
W'es+¥ ey) -W S-¥(e-y) = at ee ee ae ee 


9 OR es 2 Ze 
Where diagonal bracing in ured Fig. F shows the action of 
alk the forces, @anrreck buy Wand the ntress ow each fuuce 


f s A f 
WP PR. Set. Sere Re oo 
2 


oi Drurk a bbe diagonal 61, = : S= P’see 46! is Pp’ = : 
a Be-*) *Yaxtsh” = ( SF aya ------ by) 


7 
; | 
p +78 JStlowe Triass 4% iy 7 ” Jie 
Oe => 
343 Fe 2 2 / i. e vee i 3 
aera | ane, ey" VN Fees 3 
. ate \ / \ y ey . 
a - 7 
s Ss A LS pe / / 
‘\ Ke oo at Pas “ji i 
vA i [-) € 
y 


oc te : | 
sor gag Uae tea oP 


g q 
. 


We above F gure Pe SS Ate ee of the forces Ove Ome 
of the bridge calsaae ne agi. Wan areca eouecns buy the travelling 


will be hls eenekh Ove Ae othe ie 2 ane not draws 
A meus wk. wn the Gaidae the fondu moment 40 
neatect wheut er taeda load docsie oe sak Bald Ao 
AE get Abe ¥ ptagenes re Ahve on} 
Rordr . anwhverts. Dig. l 1 wr e Amn = 
ig eg a eiiy Bae th ) 
Starting at the feft es cee with Hy= R,kan 6 aorwy tS 
we Ree, aap chug Ahe above Welbogroms wf forecs , thak 
which smenement deercares cach time 6 (wr wo) Le 
We mow write out the horizontal -» Rs 


H, = opus’) Nat £ = apeoags' £. Not 


H, = w+w' ff fe $ w+ a0’. £ (1-9) =- w+w f. 2 mee 

H, = (ose) £ (21N=2) 4 (Mes ii 2)) = weno F a(n) 

‘ g m({N-w uf 
Swe “ase e+ “(W—s Dd Be (1) 


¢ 4 mi Nem - ao’ +1 o(n4y 
Han = (eon) fg (alee Mata) = says’ €, ns lhetond 
a in oc a a i ata slay Sh nr +)" nel LN Csi} 
oak Mas sabia Roe: Law dese et Eoes weance- Ae diag oma br 
Alone towards hee boft ahukment motead of away from it 
on, Wee Vertical rods we Pac 


jr _ Ma R, = (wr) we 


gn 3 = wr’) NES _ (ws +w)= (w+0')( Wet 4) 


14-5 
> ~1)- wee’ = (w +00) (ME ee 


= (ww +av') (1! -(n-1)) « M+)" ee A 
De mmece’ 
Ate hove wWaticie MIE hand’ Khe Abiessak Woe ere 


cE kk, 
i es Visco = (wea') (Nt m)o/ey Le 


Nt 


We Con get re Aone Kecautes Ain Kaleinag A Archon 


S= S,FiaA, enthug the nf peckisdl Suid alabk gt blbchal ellie 
of beth a Be hen | 
= X20 = Rh, ~ (m- By(ahe wey NS sc poetic 2. Ce) 
Syest € H. ee ee 
2M= o= R, a ee Er = (ons Jlaosao!) %. che Mh il. gy 
Fue avaees avs ene Abe Aton Bering kahve rPouk: the 
pom stcunoased. My rit 
0 =(w+w') N = =! = (m=1) (w+!) +V, fy pa aN 
os 6a (sons! oe) tee Bote ITY) 
Snom (¢) 2 K SS 
Hk = (v0+109') N (Not mw af a) = (w+) 
H ~ w+’ a m (N-~) eae: Tagg eRe on re gr Ue Bt 
- k ZN 


J Max, ve \ OAC oem nates Ae ae Aaekwon 
a Sanee- cuter. setae tae ice we ee occurs, 
Taco pgs name ary Sel 
by Ane Koawe ree Atkaerrer wy X 


Pe Tae "kn 3 geet the nan rtiers an wn the chiagomal 


Be pele figure Ave bridge A> mee Koased at nr and er 


aie ie ang produces forces Athwrw 6 Aine rte etna 


il el a ee Lo 


g. 2 + thoes Meee 
: eF ey Ae ae rates te scopes “oa 
fe ahuss m ree re*™ vertical ia made’ of Awoo pant, 


one frow the Sprite ob tamed by oa ya i 
m makvoro(A wi & wo{ Zt 
ee id Tle a" R: w': ; Newest 


. HlevZ (= (Not = (may 0’ x Newest ag = el z 


Up eo he middle Ad = 
V,. = UV, + VY, = wo( Mtl) 5 wa! (N= mA foe ces eer rt (23 


ae wrth Le ACen from eq. a | tak fer aie see. 
bee ea gata towakaore (A) 


whe ad(N-B NM) Saye tM at 
2N 
iy a 
+ ’ ~ ( ~~“ Pi 
T.-M 2 = wo = ( Net) + 0’ 3 WN AN di ite = seilol ien’ Ggt ine 


gy 
VUTTT/ 1 


Ae macnn, A DAW teaming ow A 
coule as tm 30 Stn nhorkex ae Hoar ie 
Db > toaded bu Aance Ae pheans wise nin kis: eane pies mt 
Bor he sonal aris Figen Avave any VES at ee 
dinemiotad by the | pron ye Smead bu the 

a eae 5) ESS ao for w+’ 


T= sions - mn] Z = in oe -w) 


hak a mol st Wee! : ne i p ni Saas Ee ~ mn (m-1 00" S 
5 a oe IN "k 
ee: 23 iat ee cae a 


ay, Ae Soneg 0 eau sions Ane Tsa5 has Bea. auyrored Ko 


Arar ow "bs Chae. chord. : Jy: At Asked a8ove Ae aye 
would fe Ae LAW = 


at already 3 As 
ae We 2X neal. Se MMO, ble ay rapa cad. -aouee 


Sere SP e the fad Od? On Mi, ner xxxx BN Suk 


moto nm . Pe of the taaePes Kas ool Neg 
be ak Fe We distance eas tig? Rig Geo oe Bea £ 


Ahe rsristanee of the eh i eee rahe. edeties pone ehe 
Anaveltiong Load W> 0 "3 (N-m- -1) aw" Nox. £ OP font 5 he = tin) 
Cron, Ahe Jrermanent Load Un,= wo Net UMW = wo (Nt we) 


Soad On tan Se Y= Vv, + = wo (X'-) + w CN-su} Basen 9! 


Qoad on Gatton Ve = wo Mt an) -w ‘(N-w) N ant 
whe pe chen A> AO+AV Now mated of AI+0' 9 


Timber Arche. ae 


a a ae 
31 i: , 4 z 
ph | : eee He ee oe ast fee ee 


§ 345 


i a ap ae eS 4 iis Akasa are os sue 
5 rata ted 7M: oceiggiiaees 


Ah a 24 oly Tdy 
when yet the moment ow Ae 


On aan Sls wale rack <n 


2 
w pit * Sa — 


Me = nO Me Ke ee ae _ 
Timber Spandrils 
uw w 
p82 Ww’ ww’ ww’ ww’ zw 
o z 2 3=7e D4. ys Be Z Hf 
$346 “eg / \ eS: 


aud Ne pawall: : Pa e. aw ah Aare At pacecaaia 
ikroonts ABD ‘other Rall soere Seve loaSeS : bipd ap 
Tf thew more Han ta of hae Gribge i» Loaded as 
Wh usaex: Ane eg ane, Au Ave ‘gaatoabeaice 2 Wie ah, tks 
a do Oe 


Mas 4riat as uate as thew avon 
AQ SS Di Ber nibes Ne ncVied visb>sade thee 


: 149 
482 ita ale: wee an apuoond pur 2a at PS oe Bnd eg S| 
$346 pot pS te produemg a ohearmg force tel.” sa usk Ge eee 
Bu By the chiagowals 

ye Bee ale eee ee A of 


: para phe Bias iocdke be al a dietadtee: Bt. Si eae 


colt We tes ap ADMoverrs s0tui 
£ diagonal Boaod eau es he iupeo east 
Ap. a age 4 1 0 
< P:-mw' 2 RES -f 
S. P= as’ sale) ns 
Me te Akieos aw the diaganal 4C = [= pass oR - so= (4) 


whee $= 

aded. beyoud ¥. ms onto Pause, Nee: Raine 2 
Bat dip f erent direction , hak da , thee Absvalagee: Aaa ee 
au ayuoard juror . He Aes wore mon fall Meet teas 
diagomal of * eee i= nae! = mti where Sa 30 and 4e= 4D 


2N 
De u™ werkecal eee Aiteiets Jack cap. da dbek® able lee 
De viol ow the wt 2 the shearing ices nonlth: Aawe 
be jo" 
Pe 


l(m-1)awe 3! o£ if 


id eas! m(n-t) 
m-!t 2N 
Py se Ce weed a Pa eae i a 


wk Aen neoiot hee 


Bees eee ak abit aiean Ete ial 
a 1h Ess oad lle scl, woe 


MR olen the wage A> mot Loaded wpe ton bulk loaded 
Sa a. and beyond wt o- a Higikiiews 

a -Asoudonked the night abulmenk, Sue to the 
Ef, at ony 15. ddiowivans | and ave Paws 
ites = 40° ea 


450 


p33 See Avr ena-2rowr eS Jnon Bow Stu eee re yd 62 § 319 

§ 347 Ste on of § ae Le acemate 
anyhied ta Air $347 Aeoanse ARe rcoseXance + ue abil 
mals 19 alway wevical aw the Bow Stang nher~. 


: : ei 
f434 Timber Lrers ak : Se 
$348 a a 9 Sey Uhe active moment 
ba =X Hy met equa Ae 
r f 4 AAVE ment 
sl wn U 
ey Riek will £ 
Ite0 3 1! de whi w e Avra ce 


\ Ba | an ond ov. & 


Deira of. Forces ou A 


e Hig ot 2 but Pp‘: ane, 


bs) ec: Yo uw ep oe pe B.W Hg 
e ae $ 2 ge2 38 B 
BWA ie Re Gadbeci siete feve Aa 0 ere tieneeene 


ely ts Ge er 
os (A) 


She force wll $e mnviformly dintkribured ee 


2 2 1 
Hay - an + AX, + Uf + ON OM, + AM, + AX, ----- + ae 


2 2 
= 2a(% 1% + Yynennra ss + Kg, : as —H4 __,— 
“Ny 


2 (G+ ™, + Xi oeet 


151 

4 he Yoad on the post at A 

F = W + H ey 
Bag -He,) 


i ge g - a oes, Bean) ay .=8 eS 
Mp2 B48 = Bln tl i 
2 ope 


: digas on: Az Ww Hy (m-1)” 
fe aes ol ee 


P's § » H (m-1)* AE ae Ve 
Aeoak an Cc ere ND Geyer ey ¥ (4) 


JP wwe make the iaudikions Aiak hire Mandl (ad. sae tock ane 
Cc ra ve PS ro] ae Be Hy- m(n-1)™ 

2 Wf (ami) (m~3)*+ (n-5)*--- +1} 
om whiede cant, a> mar be sean cuchaw From Equatvow(3) Orv 
j fom (the Dregrane of Farces , ere os ays (Go) 


14.36 


349 ie Ok ee te 


Consider Sue forces aky AVE 


= war cao 2 pursue om the 
a Re energy and ential AT 
Brut of the ribs wor rm 8 
ya 8 and of de = 7 which we Agedmpore 
f avke o components ane Tear 18 
in the dureckion af the »b at! the fivaer amd & da eauak T can AS, 
Me ether Trades momnal bi the wb ck 0. 
Anaee AO x6 “ey Amodt too ds | Tedd = T ee. Paes 
to Bee Lower end to iohich must he added the imeement 
whack comds from wir = wdermd = wale WY 


| 


/ 
4 
/ 
fe, 
< 
— eee ae ee EE 


a» 
ty 
47 
“Zi 


& 
t 
4 
i 
| 
{ 
l 
i 
l 
| 
| 
F 
| 
y 


$ 
u 
é 
ey 
a 
Q 
xe 


452 
G, ‘ ; 
p436 a otal Averrwnre on Ane cowlermg fer Abe distanee ds 


> 349 a Ads = wds cor 0 ~ Trow a8 - but AM do. & ; 
GS pds = Mw Wy er8 7 & 
a =. w ond LT 


% 
en wean 8% fod Ce tse tote EE a2) (1) 
Agen Se ene walue of otare Ae ind eos, Os 5. 2 ae ee (7A) 


So Fund Ahe Akal wertical {oad we mot decompose eae pros make 
its wertical crates hag he 4 doe pad nor forvgoutal component frdg ar 
arn dome at E, Fhe wortieal component in pdr tos 6 Link dr eor® = ole 

. P= [pix oii hinn: ale 2a (@ 
Hf the Load extends ty Ue: hey tower Hy2 0, amd af Kap, ro he 
fo 


wnt where’ p= 0 Pe (pdx faking y zo) ..--------~ (ZA) 


he mg A> Aupyrorted 
PP ge Men the 


hioduiatosat Khe, aukaw wat 
Ne 


(2) Greular Arch _| e 


488 $ 
ft a 1 Ae y= T(1-¢e8 0) j Oi £4.(1) 
w= 7 Su © ' = weor® - = aw dn, 
Y% 27*(1- ¢0s9) - 


x= sind 
tae tad t= weor6 ~ 2 fr(1- e098) T(1-c008,)} “ 


Sa pe fant tg 8]. Hee ae 
WwW too = wo. cee eee $. = ashi. ee 


OR &. 2 P: (eee > hu Xs rraw ,, ay = x evs 8 AO be 


Ko 


153 


1.33 peda = wr df 2 ton’ 8 co2 Geos 8,4... i sao bee a eo ee 
349 Qeos*G8 = 1+Cvo 20 », Afom 2 O)s 2 tan 28 d8 4, 
C20 20d0 = 229 0 
fppote = wor {0 4 tate 2? Aan 8 ea 8, Pade ig 
Am 282 24m9 2028 
Spte = wr [0+ Anis O09 ~ srr 0 200 8 } ae 
Ps (pay = wr {0+ 0482008 ~ sain 0e0s8 0, - Sita 9.0000, + virB, 002 9,5 
%e 


= wr {0-0 ~ r9 e098, + 2m 0 car} " 
P. wr { 0-0, ~ rn 6 (eos 0,~ coo f....-.----{6) 
ape artse BCys ye) ) oo a asin 2 -~(6) 
Re wrfQ- ain § (1 = coo8)}s wo {5 - Uhp. 0... (GA) 
ns fa. (34) M, = Re ~ (pede } 
Eq.(a) pay = wr AO 2000°8 _ 228 2029,} and 0059, bee ef 
Y= TAws ,*, pox dy s wr (2 C09 B Awd ~ C229 Am 9) dO 
wel, = Re~ we ((2 003°8 rac8 » 02s Orin 8) AO 
M2 Pe - wr Le 2096 + $ eos*8) 
* Fe - way [2 "O44 coo, + 3-4] 


2 > 
= Pe ~wr [sr — oe oe 2] 


GEN) 06,4) ome w {ae 8 ot Coal, aloo)? (7) 
She + of uatnons (8) * >) obtained oa takeing the Salem 


of Ae er with ougin at A M4 "2 Ary » Pe (4+ 5a --(8) 


Qu ayynosrmate notota s the Ae ak tle arek, is given. 6 
Anaad Ale a sey ee ac septs of 2 eS Ee, J 


efleige- “Hoge a pital -g- 
v s=x(i+3-& - 38) went, ars Gama bis (8 ) 


Jn Fiz.3 smoke ces Fe, 
Wen 0G=DR-GR 

-. DG.= DR~3CE at 
0G = 2w cor9— weorG,= 1 ------{5) 
Sois Ax prrrrwwr for Ae 42 


f 


Pe (ide = anea CFGOD 
Db ts apparent Afvat oak 


the walue of- ee 2. 00278 ~ nw 0008 = 0 
Lirect oA at K » mow O20 and we fave 

eee B . 0G = 2wweorO-nw = 
ams ad om the centeving oan SA. Aal ts Aer wk off 
Mo Areorunre’ A> i Ni Be tebe ip Bhe Load 
andy extends to0 we have (Pe ("pd = oea AKMD 


She value of O,= art. coo4 = 60" 


492 : | 
$349 A Me aubyzect ae Ariat: ab ) A dveurs2d on mages 34 
amd 35 of than i a ashes ri? a AMI A? ae or a treunlar 
Bhakti whieh tare Me shieos world be clireek portional 
Ao : orrkanee Adswi’ Yue cenkre’ . Roe, 4 i 
Poof, Joo. vA a(A 20 Me ned 361) I a 
mot iy hess Ahatk the oath of o what 
of Shiak: jpsckion: ” SS. Unaware beets 


pe 
nae Se aan Sea Sa Cian 


ae nrar?¢9 


Sue Aint Cease 36 Mere moter wwer the otieng the 
of a gs eer Va ae Avtoes "Ehatt of a node | 
"Go a Ss heakt ¢ sr Netes| } T= i wf ol?f Ms 16 Who? 

$ ts 16 3 
SF ae Soi apa a] € watch iby of whuele An ca Avave- hey 
ena ACD hg pad* ws aS 


sll ying by 0, 3863 Me faction given ahover and aeplacing 


: 455 

Le92 a by ite value pe aoe — 

[$349 mM: 0.8863 %. 2. fhe 

mages ote Fh LO gt eee SOs RMR erie 


rom the equation on ,35(Notes) qe Lowe eee 
{ie at . @= fe 
‘ pate ty:4 fs Boop 


Oe a ee eee 


eg atin. Ekin, Rad M2 0280 fle 5 ox €4,(I); 
cine he douskant 0.1405 an Eq. 2 ified hele 


507 a 
EE epee wea (c-d)t = pad? 
OOO O AD Stigle riveted . Cz A 4 +1854d° 
Con di *N : t 
‘ ) only fave RE AXnv202 
I), 


Ae obre bak Me: nee 


te C) O O aN mA Fee: outer Aros ‘a 
EP | W ke d. 
0 Gee OIG ae tea 
| N ii 185% A 
ae ere ee Oe N sere 4 os see A) 
¢ 
Trizle riveted eta 1954 ud rare sil ee (2) 
id ar 1354 mol* t + 1854 nd 
t 
Cc ; 
Ve 56 - a md? : _ (¢-4)E a 
Sram fa(1) (e-d)t = 1854 md? w = Ee, ...-.---- --- (3) 
520 
365 Qordons formula rr P= oo [2e0 pt. OT - 63 Notes) 
whew ~ 


Ps a. 
vetipors: i nae 
az ™& es MiSs oa he ey celts Fee 


156 


p52o 1 ony tyt Beis a ve Ke eaat row Lotus ek ae 
eee T om res See: of Fug, 1 Wee ree 4 
Gus a > mony be: mieasuneas ines. tae “dhaeckan L. 
ae : Sy ian the fgue anid: the —ndene wakes of a 
sais Bd MBI, Sc I ap (= 300 ) bd stad ao ww Soles: ask “ae 
A ey binders , 
7 ong a uy” te awtio uee am place 
os of ha’n ee eo = HF - and 
/ duction sn An aaparare certam fackore w" 
and My whak depend avy he foe of Nee fare Tea a 
Sliced wealucs are aubiden oe oe we perimental factor a 
and as mand mM, ane WiuaOe sorte he lewor-sastion hay 
Camnee A to van wn the same war . When «asiminated tu 
wmbroduc eo; Aemaww of he salted ae 
doth tlhe faasela awit: Hath ge ee 
fi £Ueth) er Pe 
Sha smmank of Smet laf aul Meta lade of alka 
gle 22 Tat eh oo 
[Sie contral, aqwane Bema nusaieuntte hired ngs td ee 


SanettecMie pie ok oe ene? 
oo Tae Hh + 4 Oh fo eke = tbe (rear by 
Jn ths equation A-B ic takew as 
op only when b to very omall . Sf we 
; take C-D arthe ana (ree Fig2) dnd 
‘ph ecnS Giitekcsetiat cools Yee eenkua 
ck 


A 2 Kiuree doer wel moterially afte 
Fo cel 


Mi > 2 atoutt : and at De euS hats 
Pei yt F be consiSerwd a» ahayred 4 Keuinating 
aes Sf Xvo planes fe passed gran Mek AS thee axe» @D 


IST 


“29 ede at ahidiotance AD Ae AL. wee 
Pee a ae ly wi ae se ane 


ee ate roy = ota [f+ ha) 2t/4 = 


Re pte fe te Ut hut fe B 


atvz hk, 2 
a ace 
a Yi loa ey “ en love Vil 4. 68 Notes] I= aa (he ey 
Anea = thr) o vrs (he 4S hy (mear ty) POR OE 
ow ee vee cylinders , [un Pr ae # kare a 
ao dtdueek from ae i gs ee expeuments = soa), WIE Care 
1+ a 4% % zm isto S 
ts we tawe Px 55 Ee Siar 


bilesie and Kaw the rome Proughout but the v0 wary 
x ahowe. St ‘he Core of a Sa, aorthaic Agar aXnwt whore 


Sanat ona see diameten of hee Ae thaw Linder, aioe 
we ‘Case ce ; Se Ue” Aide Aucle cee Pee Xr wale in 
Aerwr of the Cogent Ken Fp ie me abe K 
a 2 12 
Ju the Pinder r*s a 
5 * fs 
Hives <Pa fs ; P = eee te 
1000 Fz 4oeo 72 


Jn. the care where Phe hetlow square Pica jlo cadets 


Jqmore Kes Cobra cer ee 


Hence Pia i, Bi Sor ad oA $ 3 
| + Jese “Bo ig j,oce pt 

mt ‘Bakis and otherco ttitak: hate 12. mot worth 
white ae tae ae ew Phe formate: ot fetlow cybrndateal 
and twhlow rguare cack mon sub , ad wa the mext to 
Ae Last cave Ahey awoke wre S 

fs 58 Gad ac ee beak) get 5 
P Sees ee easy fe oh 

cc aes Foe Fi 


ee ee ee 


£ 4 

j = Bf ate = 43 ay “ bh 
4 T : Ah? 5 as 
se eee «ge 


pe Ae Gee I, (of tthe ideo) = =F 


oy de I+I = (+ 4gyek = 4 eh Auk Anca 4e 


where T, (0 endr) = % ‘ 
ce OF ej ikon) 


Te (Go $) = BR) and Bert ad) 


. a 8 Xe he (4+ 36) SS 1 eB 
es 2t(h+6)  '% h+% 


icles 


2 


dinkanee t+tv2 = t(+v2z) 
A (147%) 8” and Area.= BA (14-72) 


2 
- Ye 4’ 
fe 12 


I= 


aa 
12 


Apa Se 8 ih | 
Ware id thealinees of metal out by a fewer 


on el Aothe aara in U(2ee %eovec 8) 
aie ee * 2c 8+ cosce 8) he Qua= 4(2¢¢ 6 + eoree 0) Me; 


159 


abi 
Artz 151 Notes t= zs 


Wag lectang ANve pn anerkia of the wr 


ne whieh we deo when Aickhueor A> 
oT wer amoall , ute walue being T2 Bt", 
E a we € T= 1 Ag* Anca = A+B 
ak a ee 
12 AtB 
ee pe 255°( VA, A 
oe tre Rie Se) 


as 1 a + ire) 
Qrea = A+B 3s ee Al A - AB ) 


iz(A+8) 4.(A+B)” 
eg Hrckwess 
R > Radius» 


yo Ce . of waduante 
ie a i TBs ia 
¢ A,= Qvea of owe quad an 
() and + ave e 


Aa = fat LO x Rm 

ri 

2, RETy Rt (om a8 

a ay ah, ER (Lomo 48 = 28 [ps06]? = 2%. 0,636 
TRE 40.273 TRE SARE 2: 0.636 R: y, 


a’ « . aa 0.636: & ot R 
1.273 £12. 0.636R: Yo Sy Cece RR: 


Pre ave ree that the newtral aria ir half way From owt bout: 
Be Wiiient a anerkios of ant quadrant 
ee 5 5 Ri f ANve Sey eee eS oe, Ae an 


2 u 
ae a 21,41, 
1, = 9273 am RA x(t R)* = 2273 K FIG Logins Rib 


z A 
is (Fog(ae ae) = ne [* a 46 but, ace figure, y= R40 -* 
° 4 ° v . 


ils ae | * (ow9-4) dO = Ri | (aint 8 orin® +4) d8 


160 


4-523 but Aw ?B = 3(! - ton 20) tawtols d+ = Y%y 
$366 ore Te (EQ ~faoat rind) do 
Cup = Rt e-¢ 1 Arn 29 + eo06]* = R[42-2-(0-9)+ 0-0] 


“Ts o-i7 Ro, 21,2 35% RH 
214, = RIK ( 0.35% $24S) = 0568S Rit 


te SHS RE RS 
ON ee, - FF me 
: 273 Rt 
xm ee et 1 
A, = Qhwea . wach queadaaint 
Are Able 
a Ph ee Medes of ott each quadrant 
1 = ” vy " Aah be- 
tes he ah pkt 
i, I,= A,R* = 0.237% Rex R* = 0858 RU 


2 21,2 1.716 Rt 
abe y* Rede 2 ee fy 8 Back m= R (1- 4nd) 


aap nx (? (- Peay Ab = KL L4m0 + Aan 29) Ao 
Suk srm*O= 3-3 00420 = ancl 


y } 


“1s ah (AQ. eco wey 
= Wk [20+ 2eor0-4 mn20]? 5 [2 F-042(0H1)~ Z (0-0)] 


wile 0.3564 RU «ATs 1.4256 Rr 
ee 40421 ¢ sno Rt 
a a ae = 3.1416 Rit = m™ 
A LARC+I27IX2TRE 2.546 


= 0393 R- 


rg & 


“So frac the distanee y! owe AB 
pee a ¥ ee Be 


Ay! = [yntaey 
SEREG wy) =e (R RevsaS 48 


+ Y,2 Roms, tom) R ta 


eltaig he axr cD wired frrree Promah ee eng 


~+8 
524 = { ye Re 28 bik ys RicosO~ Rind, 
-6..5 +8, ; & 
3 a Aan 
as Rt on 0.2 ar er 2 


4 
1 


Buk ear? 24 4 00020, Le Ri i #7 eos 20. 2228 20094 ral 


= RA[ OLS An 28, = i, ets 2 Aw2B, 


\- ‘ol RL - sintentaeaite ] Feet 9 for. vbocomfown woth 
De motation of re kenct , a. Tika 


2 I ook I wee be Am 
aN race ~ Le arenes a 
0. we v2) AerioXance MA VAAWA imate Niece cs J2Ome 
above and Bolsa Ar (Ave Kable hile ple des T where m=6 ) 
Ma f. (EF AR) 2 LK (s+ $AS De ae ee 


Game eat amerked segmuntal trough aubtinsing tbe 2 ange 


T= fytde= [R? ania®® RAB = RP Carn oO 
Auk Ania*O= 4-1 00 20 


T= K) 4 


+8 
E [449-4 cor 296) - R[E — pon 28] 


= R)(0 44 rin 26) 
4 


= Raw sand % = 4 = 2 Rar 6 ; + Re Find 


ra % “ar 
rs = ( a oe ee ae 


oes 


~ eae Oo 
YT = Ri” eee ) anol RN = os uf 


ye A Bs sg) hemes the farkor By whit § bee de 


oe. Tor: AD gk Ay RT, (i— au2e 2 


162 


537 a4 ro Ahe fre Leavi we anritrvduee <a momen 
Ir Py > ’ . 4 
8 373 e Bu ] ak ADve qr = M, Ss owe OF ake clone app 
Ne ace aw the amafe 6 
: = he! J 


AO? iba ak Make nwo“ 
| M4M, — rar ak wil » Ake ae 
Vest ieMe. lepests at will, chauge chee 


wm proportion ko Ave aworments, and Af we ; 
PB Oe be 40s tata Ocal) ade Cane 


& 9:0 s; Lwew'pr . 


0-6, = (\-3 wen, 6 “ Aw +200'- Bw ~310, _ w+ 40’ 
2 2m +w’ 2(2w +’) 


$539 Case 1 See Cor.I Problem I p 10% Notes 5180 
§ 374 


Care IV ” _ 


n VI 40.104 Noten § 180 


Orea BarPons ae = (1+ 9.273) 7 Rt = 4 WU. 


She mentral acin ws phorwn sn there eee 
on §366 to be at Ale widSle of the dept 


Sot ACE! be the meutial accin with tthe metal evarcing a 
ak the angle 45° 


If 5 nani AD qrevented Mien Ate tier ABCDE 
ar of a micas and a furrow 7 epatatenk Xo a ech 

, v6] . . ‘ ., 
ABCDA , fener we w en moment of resistance of Mus 
Cell whieh we wll M, 


463 


M = -f. a ; Bat I= af (Rt As) la da be mpsege ced, 
i = Ackhial Wit>D 


ye ¥= Fie) Abc%)  R- oe) 
ys [eb te) 


Pies | “ho gaiehe Car O +4) d8 » but cor 0 = 444 bor 20 
= aatt, (Rak 00720. iia naa 


= 21, [9 44 rin 28 - Vi smn] a Ot [ % 4 +%(1+i)- ne +%)] 
T= 2Rr es) = JA416 RI 


mM = Ans RIE ge ER _ 17416 £-R%, 
pong is ee ee ee 


2 


She total mumber of | well wi fe 4s At (where Abas the 


famarth “ Onn ry ae R f 


Moz = M,-= HIG RE ane »Rat ahha 


M.- A416 £4 BA, 
°" YL 0.2424 K0.5858 ee 
, ae narkual icknesr a Length of ane _ Zz =5 he a YE 


t- actual thicknero “choral v2 
See eS Abt 20263 FF8t - fe 
_ Ms sha Sa ¥ 0.2424 KO, saseen 5 oot af -# fh (@) 


3t he ace of the anetal 
es ee an» ak 90° 
Aken wach eeff ws a ein ete: 

M,= oe hut «> f= © [ree Won 


eas 


: "Be A=24kXr se XA = Pee oe 2 ADLER ons 
»I=%* . m= oa FREE fox each eel, But the mumbor 


. & 
af colle an Fy. M, are o Lfbhe = as foht = # she. 
If the troromng he = 65" <oikh Ne et Cenk: aor 

: M,= te a, f bbe . 

Zi Due e at 30° w Ue eames cA 
f eae M,= 240 f BEA = eq FPSE a 
oie whieh me see hak 4 por 7, on Guckde Xoo flange 
and Ahak + 7 A> mot a foor app-rwainmatiorw 


164 
B B 3 {mete {I= wh, “4, ami he} 


p54+3 et —_=— Wa nt 
G7PS. Vf - : I ; a 
a = coaey | Oe eyes or as 
steps May SH OL Maho 


TRF qa RA a 


She queteot straw on 
nv price rxcept re 

3 diagonals Gand G, ,oceunrr 
bil ate hoth, permanent 


any , 
Trapezordal Truss ot AW = penmnanenk Bas 
oro! torte" prin Erb A dung 
Diagram of forces SLC the action wher Y 4 ‘ ts 
the travelling Lad. covers the bridge, w of 
4 BraypA 4G, S. ,K4£ = 
A+F ! 2 6 Z 
B+G+K + = 
Let w' = ve U Pransed' Load AQuak Can 


tomt on § 01 6, and Amp pore Lorde 5 and 6 Loaded . 
wea = P= ~ Abe rerrdtani ee of the abulments 


hen ware. Ht s0¢40' 3) e+ R “4 = Wt’ sa hppa. > eee - (2) . 
Se qgreakert Brot on cach vertical 5 hoe Rs > 
So MS nap BLOC KEG)... 22 fa~-- s+. ..-. wyekeon ee (am 


She soeight K+4tG nests ak kre hottowm 1 ancl 4, and mot at 
Nee Aon -pomts Sand 6. 

Sie rakerk® streer Aw G sothl pear (46 ane ee 
Aoaded bug aw and ar vanbpaded, .. Iu PS Care Are ress Kanes 
of Ae abubment..at 2.40 Ps welt; C-X: 20.2. AP’ - mal G-X 
sohaen woiulh alsa be tne aupwarol ADrrviek, Aw K, Fe 2 Pree 
hase Ao he \resioked, ak, Ahe pom x bu re vo qrrecdco G,aw Bz 

2 So! SFr dong th G, 7k 


oe 
gf = tyme --- 2 =~ fol 


165 


Bas: 8 
549 Th age / ,. | WaRREW GIRDER 
\ 5 Leg. 7 
ei Wy : 
3 ons 
G | : 
AEF : * 
: yf {Ee .: 
ak gan y ; Aiea 42 
LLY) y 2 | lé vd 43 9 ye 77 OSS 
Gs A 2 
he tea Wing Load covers ankine ase Cure ook 
AVA at Ahee ee: Represents AO + 400" ‘ etek = 


; eee pea eh ee Ae webive® fords Pe Pets 
“gee Bar fil. ina san Sie Seine db ph does, Cy 


% 
y= H+ 4 
£ ‘4 L 
H=H+hte+ kak = Hit oe SEa,.6 ee (1) 
He. 14/R* £ Seiaee A T 
nH Fire + Bet Boek = y+ Boop 
“s y= H+ Geet 


Sor the middle of the fridge M,=mWL and from the table 
ie Care Vill “+p. 70 of these Notes , when Wry even 
CMe and We (45 Vlars<0') 


B(N- de aoe Gb Noe) - ME oabdaet) . H,.* 
Hy = WF (0410) w- 42 -- ----~-(8) 

Yo fied H.. cae p PHT 1G yes oe Liweet) = HR 
se Maps BWA, on bab lh rastO(9) 


Gi. equation mise be toms : ae werkical rxckow 
AB a ets > Se iy : F 
pa eu ~ £12208 26 eet 


p 549 Ho £ TOPO Ors Sloe Se are ares ci, (9) 
i If we equation (9) we male m=N ak reduces ty equations ) 
le gd aie to Fixed Load - See diagrams of forces Feg./ 
pe, Peete a) | 
Ts Fg =(b-w)% = T- te 
The Ag =Uh--)% = 7, - 2 = To-2 
Te Bg ( ~)% = ha * = Fin 


—) oo Ty = Tit 1) = tis ae A 2 
: m= Uo (9 k 1G 
ln ta cingonal mort Gayonl the milale. ma 


tk 


-. Th = ee oe ee N-) Saw WW Saw $v 
4 2 


Jo get 1. buy Ft Seer nbs Suppore ae the. sveckecou/ 
i re aan cutting he ee tie. Cneshied = K= ° 


aus Cte vertical Component of thie thiiag Dis pei AO 


Se Webel ee nas 
Diagonal stress Aueto b uct 
eee 


as 

e 
> 

Fy 


mae Be <u | 


i) 


/ s nthe aling foad ‘dcrwies’ lore ae 
G4 hand 
bud , then the 2 
wt Se OR Ge af cote 

i an be rips pan Fron “Ft ASe- Boa; 

I ee MA Pits CORR 3 ee 
Aw ), WY 4k nom Ite 

ss Serr Aa OM feng toe ne SOs AXnrer2 of he 


Rind Aenrion) whack Can Come on mal = 2 “aud ee 
worl v he eum of the rtrerses wore Come from 10" ak 4 


and w’ af 2 and = §, 


1617 


Wp s53 Ler Pe reristance of abutwenk at 12 when Foad ir ak 4 only 
377 FP, = nevistanee of rame- when. the foal w' wa ak 2 onby anol 
for FH, Ke for Foud at 
: neva P : 


20 


1 onby or eA 4 S= Raed. 2.3 é ws 

yf ts: wae = 2 1. S=(ReR)oceG = (is8)e' § 2 Bae! 

Bn AM ras Bs eo Sy o(ReR rR seed aferted)en! g = 6! 

wn XL: uf Ht gettiP =u woo, hehe -€, 8 2 (424m) § 

TKreve otrerser will Le different m hind from tore produced — 
ee aif Ah as reached, 


wyona ttcnk. soar they bal 6 de bina’ ane BB Mass 
caused by the peunanent Koad. 
fue comp bete Able for a bridge of A2 panels DA» Ahowrn wm 
avis 


Untiike Lermarent Load Like Permanent Loat 
fs ape Sy (142494-.- 41) Aste = obs s 
S,= we Syn = Mo = (142434 ----10) w'S, = 55 wes 
Sy =(I+2)w'$, = sw'zp Sy.32 So a[lt24p4---- 9) wh 8, = 45 228 
S, = (14243) w' Sp = 6 10'S Sie S, o(l92t44---2- 8) ws, a 36 3 
Su = (1424344) wo’ B = 10.40 See Sq = (14243+----+7) v5 a 28 a 
Sg = (142434445) wp = doa Syig = Se=lier 43444546) ws’ Sy = 2) as 


, or M0. 12,20 


woke am Ne alove Gakimiens ato change places ar wold 


ASve feadmngs. 

Pia nes Ae Bewsade < Ate above Arle ree hucet 
Céuse TT Wik Abe ard from. Fg.3 , whack SE ces ASve for0ees 
ou one of the bridgs rohen the Poe oad evvers Ahe 


auvtune fridge, the rtude wilh Le able As work AAs out 
without additional notes 

i. ae Figs 

: _ J of ot 8 


S/O, 


S99 — ee 


168 
562 CaseZ , 9, Th Pay Been howe. Oe alee 


« 


a parabola iw Ahe mn 


aotintle. wie the eens awe rave 


ARE Fu 2, 


HR wee’ p L 
Ie 


2 


2 
HW werwity 


(o+w')X% 8 
de frre hs oat ak aay het 97. Be a ote 
H , amol (0+40') % art hers 2 mihibrvan” and pre 1 4 
he soroportiowal to the Arcana EFD 
aT = oft here %3 

Sl Ad 2  Ndlimade cantiteot soail eleaki Ag Dt hucilt 
oy 42 Beery, wnnifo AvatruiButedl , amatead af 
Ye ” oie ow “ow well e an qty gon Ale werticer 
Haineh;) seareweltly yi Abe parabola, ) 
Rolling Load . Sup poring ARO Xo ad tpl tone are cae 
By bof or Otund (ree tg. You wert nage) thew “tue 
qreakiot Ce PS mathe sm nertiead ACCA19 AD Ahie % 
extenolr ap Se aan as ee m-| P 

Radon a> Aesoror <a Can be otten a) on 
Drruniptrow ADak he ee force ab and he Mm AD 


amg 


169 


pe 64 Fg, 4. Showing porees D7 right end wher load comes up to and includes Te 


$379 . ae 
G | ea 
eds * = a i / 
\ te 
\ \ \ 
: ‘ ‘ \ \ y 
‘N \ 
a ie \ ’ \ | \ 
NS a4 \ \ { 
~ x \ \ | \ 
0 ee \ \ 3 ! Nae 
TT, 7 2 2 & Te 7 vet 
@ Q @ ey ; er 
ou of A ea a 
2.0: ‘ 
N 
Both 22 arrumptone ve nn RU0C A? ee pe ea AMARYL R 


impacting Ty. 4 from which it is obviour, firet that af a 
foack ret ak na it wll dinunrioh the tet an the wth werkeol, 
lidtond. that. -a large park of ASe. rercotarice of Ahe abutment, 
= Q. goes i he tenaet along Se how ,-20» 8 wevkical tomporent 
Mice Ae Goi ar not Frorigzomtal an Ae anppe. se of the 
brusges formerly AOrerred Ar. 
Sis get Ranker exprersowr 

Q: mn wo £ oe @ +1) £ me a Q = SES! cus S Sri See @) 
Jf we aubtract frome Sur, Ne park of re pernanent Lon. 
whch reste at m , we hav for d Compression aw Ae arth 


real. an re 4 aD = 4 EE nt gt Ie ees Sk 
fies Tp eee ar. Cr) 


aan diagowak Ao Af we anal icgaby ae f (2) aps AAI Lowe 

n (“ ote Pe Ss mln) pts _ “ u(“stl 

a! sol ts co cO - Oe  F ag os? ...-._ G) 
Oe Dita Ay watack tis, or miveviorn anans Be Aeen frome 
Fug. 4 Eien wwe. mokee that. he fovee oats Btw, fran pout 
of Q. corde 0 which hatter workol $e represented bu Ae 
} oP mR , 

Ts fer S = Greatest stress in n* dugonal, nC, 

Of VACHE mene ee an wy Big 4 aE PS bu a plane A-B, 
Conrider the bow a polygon which ik either « actually, or 
wirtuotly ; pro duce EC je from D Lut frakk DG a perperntientor 
aw mC prooluceal ‘ 
' Saks moments gs eS D;: Yvo of the Arineeo ack parr 


1 
5 


psb4 Chrsugk the mont BD and Aherefore Ae oreo aclu ale . 
$379 ike Sas eee see anne. Sto cncatuce? of SKE & An " E 
di Sxp=QxWo © Suz SEND a. 


P : 
Ts rol NWO =z=unrD-mN we Bike AIAN See Prong Dery ; 
Fs Er: FC 3! ey me 
-mD= FC * Ea in 
: a €F 

Sek Py ae ie feng th. of Ahe ui workical , 4 a fongthe onsi)™ he. 

Ss aoe 5 _NDdz tt % 

a * 5 es es N(Y- B a ef ves tie takes ie ‘wy N . 


Te find p, we have frowy Me Needs mG D 


p=uDx amd = wd Neve = re Y. ath Yess , 
. vn (ret! Pe 4 Ef Pg £ | 
Sum Beat ww! SLR ae Oh)» : 
(v.-% Pe a he, ‘5 
y = w’ ats) av Tees) § a | ale EIN wll uos-- eee A 
eg Sy a mn = [ e (N J] ( ) 
“So frinet the gueatest Huet tn the rh wertioal’, Me Loadk muct 
f 


Extend ap to , anol Anebudle he mt fount , Luk mot inmeluda- the 4 
ah Ck 4 any plane ,as Ly, te bow, Ke and vertical, — 


dnt Mahe dic tentinee: atbiede Cais Before i 
De Ti 


> 


Vi x mO0=Q xND | /’ = Q 
Auk, 2 L jose fuss Dep 
. iS! ga & 5 aa m [um-l , 
Qi (m1) w N oe aN ‘ 4 ie Q.= a ~ av rr 


for doluar of ND anol 1D nee above . 


rie Vv’. 4 M(~=-1), £ €. _— ~(N-m) 4 x TRS 
4 nn m+ ‘| N(Y.- You 


Foc wy su(n-i t wn vi | | 
V= Vin f. we 7 =} j EE 7 ~(N--)] ian ao ad £ Sk (4 A) 
fe diagonatbs RSG. by Grshers Litter “dul titi uae ae 

"fair bridge Wer a a SB tdheae ie tad baton of . 
anda Bak hee Aton wea K > mot azo Rr , anrol ak é 
Was 53 ae Whips te Prarareg | WHIPPLE TRUSS .. 


P, 
g 
; 


+380 


3 Bl 


564 Case LT Bowstring Suszeerston LBriclge or 
3379 Lenteuler Truss 


eed ey ake the hae 


propection of Ahee Mp per . She poank 6 anak he foal 4Q’> before 
amnch tan th aeed cin cntre of moments . 


- are, Ns ai 
= ae ee 


3 Sut. 00 2 nD-m0 , and un0= Y. cot 8 


p=(~o-y, cot 0) rrr O 
She ealeutakionr ANae edr5e Are niviutar Ao thore for se IT 
> mnnnt remomr equal ; ao hak Ahe- amount 


“Lt 
ep MO! 2 AAD! 3 AW ray R %, 
nm bar an a nevre be called ideal ar giving the 
ralerk EL Power Sor Ne Amount of eee? Gee Buk 
9 lack» Aamep be At tantinetiow gud tho 4 af Bowel 
Ae @srne beloaws Ah Aoadway Ay Aahte to mkerfere mathe Ate 
water hey ee aoadwan auourneatf | 
223222000098.000000000 


561 Casel Flinged both o Crowe eg Springireg Her, we "aes Pr. : 
Hk= iW = wer. Hye WEN -- A) Seo 
j we” 2 “if Be x 
HR = Baa ee (2) idee ee A 
; : a tp a ae 2 =e 
T= Af = (H,+H,) eee AA =(HotH, reer (3) 4 fF (wos 


§ 


car ye - proto eS Aas , 
Kune” ‘it 0g df, eof g. of Ahe a) ang ; 
verkeal tid ie ert wie waw AN adtuch gave Aes olueckig 
R ; ee ) 2 aotbelogram ar Se ava) Ae 

ie Ave e Ae pee ry Avi. as, the ae of 


a shows abl the forces acti AN ae 
“4 ; ey, Sonne 
he medeunet preees , Ff Ahe mitboacle half 


~ 


due te Veh ee 
Be pone ‘ ak wtmrent 0, A oleeo oned aby 
ee te R anol Re 8 a ue jomnek ae belongs Se active 
force , whieh Ae ecomporeol wnkXo Fi, and § ; ak 4. Ale fovcan 
Re and S, one Lot. active forees whisk are equivaheit Xs 
the odreckron ee and +e mks F’ and F" ; ano a0 forthe E 
other pout Rout Ae Briclae . 
Whe sprees 3-4 ,ak che pom 3, quer Balan tae Ache Driust & 


& 


2 


113 


£563 ak tlie _akbites tod. Ae 2 Lower Frome rrroboamna MR, rohuck 
$380 ack, ak Yue Crown, a kee olircekrorw of rhe preter 4-3 ana 
Gy 4-e - Ik Bull also be: meen atts Fhe Aemsion atowa Abe 
: juieee 4h-@ Av Aneel bu an equal Loree at cach enol, 2 one 
gotten buy “anak ek the other at the 
crowns. Notice Mak = his ish, 
Wi Senn. weiner 1nd iedutol gee aa: Sosa re ae 
ieee Abe faded al ag ee aang oy Bes fol pepreoank 
arckwou o : Xoad comrderneg wn wid 2 ak fanda, 
ee gon appr aaiaan AQe other ia Fac j V 
ihe uctuodle of Aue poveee nepresente Aes “Fog. 2 
coarlol Le orlelate dt anahakceaY bes ; felboroing Afve qrop heat 


G, 2 e 
a aa aes 2 5 ge ea Hhoee Apreces ; ALve onidas 
4 here han Polk 0 ee tidar ass Aoacded ive ceed 
f ; ath a eh above , ae 


pro ecerl a? po ee Ann Jag.3 


. 


, A 
B Bs 
page 
; ae : 
DK... Be. 
R | 
2 : 
| F 
. ye" 
a (e+X%)w’ aaade 


YZ, 


R 
By Lrial find a pomk cake 4 oe ts wolial aes 
srgeeoy ronal Que 4 5, of Ae fas tes be Fecuk , and ro kseaked 
Aton gia . 3 the forces P and PY w- Vie on ome anol the 
tame atroaght Lnve, BC parsing trough the teonge wt the 


CALM, Rso a=? 


a yay nS te ae rk 


174 


56s Having foumd he diction amc maginbiucle of the resistances 

§380 = R, pity Sms Ade roulwents , we ean fmol Ye 2brerr ov each 

Cox, pr ieiomey Are awerhiod of neckronr , Ov As war howe awe 
the care Whurtraked im ig.2, by comrtrnctiirg parallels 


peli Woe Acasa’ ea bovees af rtrese aw Pg. PVs oe oamol 
38! by tafendg Me alachraie Aum of ANve AX? die Xo Tee Ga 


Component, = p' and Afiak Eo Ate Bend: mmornnent = ; 
} A: Fl Dr p= Math aw - Cane an = 4 } 2. a wR. 


wand from Kable p 525 VL {rms Z = a. T = Ag 


o> ore HY ._ p 
Pp = ers sy ts 5 alro p=} 
8 
ae HY 
P= P+p = ai 


a . 
he'd Aericzioin “ow AR) 0 
70 AA C2 Aenrrorw, we dave ar a 4k, 


Ce Se ite 
ds BY ws .¢: >) 
ery, —— tT B:T Yi Y¥ Yar 
§381 Y" 6s 2 ee 
. <————— ae 2 Se Y+Y’ 
Y M5 Hg eee - - ~ eee ee ee (3) 
Fig. wits 
=~ Va Bae wohue for M mrskeak of HY avbuck 
= ‘ ) 
bs oo lp [eX 2 Be Se 
nei r= y [ating 8 PY nis 


al {p90 (13) sex+ Ey nearby ' 
{T =Heee < = His } 


= coals Suk As neckional area of chan for H 
40g. 2 ; A's " i ig “a “ a 


c'. C ssw A(x + 24) :wAy .! c's S* + = O41 Me) ce 29°): 
{xt 2py } Re a , anol “3 = % ae (1+ 54" )* = (\+ 8 i 


Aeveloro+ as Ba Ae Diora Piao ana Antiwita 
of ) 
fon eof ef vw e a e ) Wrareg only Aww owas» ‘ “3 


yr 
‘ 2 
Cs cx (+$4 sete.) = C(14 5 4) mearky beat cpa chs el (A) 
Set A” = woniable rection of Naw for wanrable publ es os 
” s 3 oe: : reseal ae oe eee] mPa” 
5% ¥ MAMA Ye Bi tr | Tat P * aa = 7, 
+ Ate THOR at A’ ATS A ) 4 au? 

” ‘ C ‘i hack @ % 24 uh 
C st: faa adr: wAx 5 CsA A(i+ F4°)* ds 2.0: E(u ied 
eC {* 2 .£f( y* pie ik 2 

CaF | (rd dee F Ore) = 8 erm) = So, 44H). 
“* 2 Any ® I a Ba le ae ee 
chs C(1+ Eh) @) 


If MY DrPAMnNE Ahak a wine pabbe can rafel, SER a. wets 

of 15000 toe. to the rquare auch , anid wrt Xo Frc ADre 

” of C. Awe. Rade (Ack A= orca ai ag. mchesr ; f= 15000 
C= 12Ax x (wt, eu. am, mow) = 12Ax x 0.277 


aheo Af =H amar Ours the two equations *o 


CAL = IZHAY¥ x 0277 ee ie ate » XIZ% 0.277 _ Hy x I2% 0.297 
A5 000 
pre) ee ae find the wale armed wr £4.(3) 
4. 5°03 
we fave ¥F500x 12K 0277 = 14958 = f= Ht 
: A 
For cable -tron Anko os ie. ~see E44) jp Arrrnto Afak 
a9 


f= 3000 X52 x 9277 = 9972 = = = 40000 aveanky 


—_— 


—_~ 


p.279 
§382 


SN 


: Road Keamnater from Ne centre of Are aida ; 2 Peng commiclered 


(76 
VI . 
AVILS Perstor wat ridge corte Wey teffereing Truss 


bac’ | Fag. 3 wh 


\ i 7 
YS : ae 


& B 


“4 ak PRREEE! SER. 
5 lee ve App teal Alechanies g 340, awkine Blin hier no ae 
Mlecviasdbbetae Luxek Luv gakvon of Ade bie, of AN» budge 
hak far appeawd mi prmt; anol he following 42 targely f 


Bnidge. Bay Feavma Ax out of accommt, SY aa108A : 

will’ he made ow the rafe oi ar ts the stiffness of the 
, and ‘he eleulatiow uvll $e sien Ae 

The Girder partially loaded . Set EB a 

Aepresent roe ee th al Aha Po attack? part > sc Abe eng ! 

eat aud BD that ‘, Ahe ay ies na Ler wo Be aiforme | 

atenre of the Asad andx Redistancee of Aker pow Ao exe : 


x 


§ 
Tit and a megakive quantita whew the Loacled spark 4 ‘ 
Ahorter ae wm fag 

Serudhs ehee of the Leam tema farkemed, 20 ar ; 
Xs Sc aneapod be of wertieak ole Pacement , Loackel reqwenkt 
EB 14> ecomvex downwards ,anol arnbooole ol Aegmenk so tee * 
mpwards ; he Loaded Aegmaent tn aw the tomdlebiow of a bean 
aupporked ak E and B, anol wonrfornla Roacte ol with Axekr> — 
of Ate weg he p~urkamed above the force acerked fetweew 


117 

579 Apis ae anal re Rain ; and the arDoadeol Aeqment A Fees 
$382 Ae aT ite Paar Acld down ot B anhd D0 anol Adashash aware. 
F Sap. an formtyu distributed force ack upward , Aernag Kak 

ve) Posune of Lac AtarnanX 0 ak i wuddle spor her A for 
as adel Jee ngs ov Due anboadedl Put, ae 


EB = @+x 
rks gore Foaol ves W = wo (0 +x ) 
land. Ake ankensrky of Ne force axcterte ol Aebin diac: re qurcler anc 
re how’, ao! = “2 (6ee) .. SR eet ya oo Rar eee (hy ee ar ae a @) 
2 


id ys . , 
Bhs AY whee Ankeny xe) ADve aero Le AAS ANe ane 
BO uhsac AD wad is ; east comaequent | geod, Ao 

coble 4p. 246 § 16! ; Afve qreakeak anoranent af § pacar’ of that reg 


oS pe Slee) = wee) (e-¥).....-...----(6) 

fre FRO SSS of apwarol) foree axerktead bobusedin hes ekki 
and B : . ceohae 4 
eg W = ee pes ete le 


ad Wu alro is the amount of the wet foal ow EB, ber Ake 
exer of AQve See Loacl abowe ASre Apark Bae Jus Ae Pe eed eee 


Vue Aalf of Chis quantity p oe 2 Cs ee eee (ol) 


Cthe walwe 2 Ale > oor ise eat Nee Aer awot 

er iten. Waee; hans sie ae hetrweew ee Se a 8 

br Ae quider at B, and 2 Ake lower Foree Any ao tebe 
ands D of Abe queda ie Metol. at st; spomk of aktackanent 


We inte vey of the wet Load on EB > 
AI +40 = rid dea Being Bo es eee ees. i ae ee 
and Ae te Hh. of Khak segment ber her axe; ste aneatest 
momen oft ftecure eld to , tab 2, Pp. 246 p161, AY 


= (w-w') (C+)? _ w (¢+¥*. (¢-%) 
M, at 2 ares “PRET i, = rage. 
rar 


wy ascertained , that Ahe gavakeot rsnoment of flexure of Abe 
Loaded olwirron- of rhe iden  obtans “oven 2 = 3 , or 1 % 


of Ahe eauiz a Csoded. » and ANve greatest momen of flexure 


118 


pr19 of the anloacded dwiruon of Ane guroler occas oseee: tak © ow 

$332 okaaak ; of Ahe igo are unboaded , anol furtter AN ab ae 

Con Awo qraeakert anowmento ae of equal magurtuole ane Opporte- 
eee F Aa 44. 


max, M, = — max M, = 


ae 


ewe 
To find x, Vf own Eo (fF) 
fe 72a lL, f % f mM . ~lese)t(e-x) 
A~ 16¢ 


. "= [2 (e+y)(e-x) - (e+) J= oO .. 2e-¥J-(c+Xeo -. Kaze 
from £4. (6) 1 ees = ie Pa +2. [(e-rP- @+4)(€-x).2] 

nee ¢-x% -(€+%).2 = o ve ath ee = oe, %=-Fe 
In fa -(f ) Ant for x ‘ike walue (when M,42 a max.) $¢ 


man, M, = w(erse) (6-50) _ w( Fe) Fe_ r2wet 
16¢ 16¢ 27 
w (e-fe)(tr3e)_, ~Fex$e)_ rwe 
i A6¢ 16¢ 27 
wine i 20 wr pptoen: Ake aottineg Road thine Fea bf. Ue bridge; 
re 


mas M, = 


ganas, Fai Wwe. ee 


If the girder 12 hinged at Khe centre we ave ee andlepen dent 
Fiokf Krtrres » and y greatest Abra won tthe age be 
whew the boak eoverr half Alle Teas e, Whew tus eeeae 


tie. boaKmnsenae Muses, amd Eh, qed Anise ApOMte Eee 
Ree ORE: Mya Me we" 


Jf, te conform aonte Ae Oba eee Aue » Ave# houta 


X fore, w'forw, M for MoM, a equariorns (t) anol(h) we 
Avawe = 'y 
ee 


F= pt ae ~. lS. oe eee 


he 


bas & las 
M= Zar. oe (mearty) -----~- -=- (9) 


weg hk frrak Kouches Ahe aprle aud 


05383 W = s,W'+s,8 | ype Slee eee ores aN © 
578° yw AB iet fx Le £0 
ie les EA fete)... --- 
te et ero be 
2 eee s, Lak Ww Si -£ ‘i 
J w’ 
[46 5 A423} then La ffir$ Oy = tfre2 5} --- @) 
ge it raf 
Wo F4-t = 7-0 -------~---------@ 
604 Ket aa nae balcieewd sine nies and pile 
$402 AL ew sf} “he Sorce Pas web aware Tie? 
ty L ts 


i zs menrtarer oo) a P when Abe spite rwuMvoves. 
ae Wve ? os NE ees AD compressed a Martane AL 
iotnke ak Ae be Ae BS ee 2a ALDrAOW ; 
A: Se: Ae eee tomspriessron tA Be nea 
: 2 5] A ? 
AMINES is ine. Aa Ahineg ; he effeetive , AY 
Ay = Riot We ie douw an Comprersron = P AL P.LP 


he OE, --% 
‘ 


Fhe Soa: hdl an drug ae Px Seer ae 
WR= PL, Pe. 
29 

i Solve Be IF quadratic for P we rae rkr wabue’ 

Sy 
Ps. % aoe = ae pl a tee os aie ar ete I et (1) 

= nab? xe? 
oe 
M=T wotxh + Te ties ay peal peo Se (3) 

644 Let 9 = retordatiow Ane to rvtacoXtance of tankes* 


Shien se ond 
Wi Ri ai @ “G= Raa fa 


A 
x 130 
\ y ) 
2653 if “§ Problem 1 L porz= vl ADF 
L por = 40 «. DF= FO*m Gd 
So FE = FoXan SE | 
Fo=- R= —_9E ——|— i..-- -- <n 


K 


Problem I Yow rimple Aime eawe has 

Fon A> aquakion : 
Mw = Aww x anol Ar represented, 

4u B‘p Cc! where We aang te BAC =a | 


nee Cnnwalure 5, . %, 
, ~ (V4 p)% _ (1+ corte A 
i 5 A = mm 26 

Qc p when x= BE = 90°, thin r=i=DE, aw BE =AE = 90% 15707 : 
DE =| Ao =.5707 .«. AE ~ 2.75193 . 

aot Ao. 7 

] ‘ 

or AE = 2.75193xA0 and AB’= 2.75193, AD rec z BAC 

Pk dks Remap SS Sie - ' 1s. ee 

ae F707 = L7x193 ¢ " 


Now a SA hee Kamaents Pay pee re Le BAC a “wae eon 
mony Sttrkapae Beliceese: Ane 6 tha equation 


a ips 2 88 care DE wo fonger = ther nadie of tte ecuele- eae 


2.75193 % AD xtan: BAC , , webs Care ; 


£ 
2 


~ a0” DE qo'x ln _ (20°)? De sin 99% , 
Fed: = 90. SE cor oe aamol ie =(=.)* DE An Se 
/90°)* =a 50, 1% : 

oe, (14(22°Y, 5B e92( 22%] | 
» T= / a = = B ak D $ 
: i BE : negll (when ¥= BE ) (ae F = 
se” (Zz): DE ain BEG 
Be Be] =F) ; 
v= DEC.5707)" ’ 

But BE = 2.95193 AD tant BAC; and AD= aD mag BE = DE(1.5-)07) tam 
fon di ae 4 
. BE*= DE*(1.5707)*Aam?t GAG. SSS — ; 


# 
Woie are DE tad BAC I. ~ ee G4) 


— 


WwW 
ye woa4 he drop ppcol from 
UP Et. pane t i. (3) 
3227 
1 ates Air Pocic = 5280 ft wr 3600 Reese = =- abe Fx. aa lreeonedl 
ir ia eypresred ww a Nex A ards oe ee ADO 
sage Xo reduce Ao Feet per Atcond ; 
3600 
ae Vv" V7H 
3600 = te PE at Neg Sh aed oe) 
= od py oy ( ) 


pO is 
hie Aen of if weet, Hrong eS LS Yate 
Sur 5 vital thea nw sg ar (3) eine. anol ig #8 ON a 
wala »’ , we Saeed 


0.97 v= 8.025 fv | Feood4 -------- (1) 
64H (1 +F) 


Oe Ahe 
Be ech b. . cUeay mouthpiece he 2 aoe peer af 
3 soe arn ieee Ade Aone A? Ate coef. 0 
ynrek me. As ee la ckiow, Subrattnke a0 rey 4G 
and we ge : 
a (-813)" = — Fetsgen. 6 oo Stn So ers Zy 


Rare MNee e.). Werbach AK 


ers A> 
ou Sore at ome ang tes , sop Me Aer oiacakeoae 
of Che a. Aa wad. 


= 0.505 4 0.303. Am 8 910.226 am 0. — - ee 


_— ee 


182 


Q'= 8.025 EE ae 
= 5.35¢6(%-2,)% 


— 


OF Ae drmoned park, st a 
g.025 oh, Eee 


Q’= 8.075 cAVh = 
= 5.35 08h. 3 17-8, 
Ca Kogerther Ave 
a, iQ. nas e6 (f+ )/Ro, ..._.- om (V) 
686 Se ain, Eq. (1) ihe) . BOs 3 < ayy, 
a » = eras wt de (Siro) 
Let f'2 fraf ten dz a (Fahy a'(i+4 af). = d'(1+ 5 2F 4 he) 
= dA'(i+% AS) tay Bie ai (vt) _aig+£) ae (7) 
he hi Vis 4) Ip . 
d= d'(As Ee a, RYH h'( +4 8 )oveanby ---- --~-~-- 48) 
esa Vevrlles Sectzore 
joe es Fle store 0 
Anexn AFL = ae coraee 8 


« ABF=Lr* tanKO 
Jota WEL = v*(evree 0+ tan  ) 
Wertkeot prumerter = 2FL+2BF 


ae 
P = 24r(toree 0 + 2T Aan & 
~ vr *( ew2ec 0+ tan 5) 


io ae = ir 
2 +(corec 6 + tan $. ) 2 
A at 
me ci= aes eon =) = hcosee 9+ ton® ) a 
LR Equatiwre (2)and(3) we hase. ,2 
wm! = et ahs Paiste Aeige wat], Q : 
ww! tesa 


Son tquatron(T) ae fquation(1) of § 4.50 


—_—— 


133 
ourata, 
Bane? Caer Engimeering Text continued 


VPext /2 4% Chitin 1894, 308 €9 5 (37 B),388) read a4 for 0.192 
P47 G3) read m= a 3/9 &. (7A) read = for =. 
fer z's Trt €0g?6 4 72’ Si72*O 378 (re u  ~,3860 per pse 
148 Ezs.(7) read M,=0,M,20 | eet read 7 for g? 
fer M=0, M=0 4.07 
ISG RI” Vine pead Od 27 OA 423 ég. (3) last lerm —— aS & for-2 - 2, 
4 w 
WS9 XVI read 2 for = se cake “ : 
/GO X/X read We aay Tr Yeos a - coxa) B xl Rais rene oe ee 2 PRS? 
170 4" Line read the ey BB = cit nate 
for the Angles BB These Notes on Kankine’s CE 
2os 6S) read fs for fe p.f GAT) ITA) wn denominator read 
$ ~ és ; @ r: WW? Ab for Be 
cea oY) ao i é ane a= nF B= Ee ee ane fran bottom read Cx? for Cy 
2O8 GC) Zast term read un the Aenomenater We EP rie read % = =4 K tfor x =6 Se. 
(3% A?) for (A*- 8B*) 4 20° § 21 lines oe mie ty 
‘2/0 & (7) Tread H = zo" tex fr 4 [pes 6 272 Line frombolttorre read mm, for m’ 
TT» ae to Pie dy fer wo [pax gL joe . _ iy - ies fer {22 
B : moar. See tas for 
2/3 GU) : o= fP_ fer c= /P “a 3 
Peoesy Px 7 ao 0 «Bahl ee ONB 6 AVS 
220 oO ies read Ts. 128, for fag. Js; Vi Aas , DMB , AMB 
234( VI read Ah" for KA K? 5” | from bottm DPZ for APZ 
7 line from bottom read fag. /2S for 121\23 2" bene from ,, Treadl Vep = Se 
about middle read P2fS+2 fw Pe fSi2\ 2% 27% 1 PEELE tn reemerador 
247 Table value of 7 per WV even 25° xX wmte — " & read 71 the denomiator 
read ga for ¥ Tr? fore’? 
280 l0“ZLine read ot for 2° 26 6% Line read z, poerz 
28% Bt , » less fer greater oe rom bottom read Z, forZ de ace of z, 
CUS) 1 f° for f 27 XV/ in velueZ reatz forz’ 
28S In vakee 2B & 3(7),(8) read f for f Oo. fo tee read la for r 
290 /*hne middle Colum of Table 29 om - from bollom reacl sin for S272 XL 
read x for x* 3O &.(/0) tn dénominatr react Ae fer x? 
293 17* ne fron battar read k& for \’ 4y FS" ¥ 68 Gres the last term in Che brackets 
R96 Case XVI of Kable Should be omitted Should be reine by 2 
as refers to ar artecle Sy ies LE &. (4) reat eo for dont xe 
appeared wi carler editions butes|h&7 ,, (ho 2 5 OS Pag - & & 
omilled, at Toast , 27 all afler the |49 13 Cine read (6/ for(S) 
8% edition aeso cos(t’t 7) fr Cos(z +7) 


184 
page orraka 


52 qe read 28, for 98, 

whe) PPE. fer p=pt, 
53  , (C)readR PTR & 5 DE) read py for Py 
58 € &% 7,60 fruncbottorm read aasects for. Sek. 
63 nadings, age ee 
66 VW under S$ read Zi git 


wre JT ff +7") 


67 xX read T= [ [xd dy = {ftxir 2vxvd) dedy 
= xt{[dr' dy'+ ee, fede dy “+f [ee di 
UW Tne read Ox’ koy’ fer Ox x oy 
W 37% Gne belo the fc es read 
ne Below the feyuer 3a. 


Pp” ‘. w‘(t-x)-- rot aa A a P= sey 
and the last mernber of ' Cach eguateore 


down te and includeng &g. 3 shoutd Se 


divided by 2 
72 last pnember of eguatcar at bottom of 
(e=xAWy 


page, Te By F-¥) 
_ ay _ ot x2 a - 
13 Glo)reai- B= eg GT* "DRG GT 
my GARI read y ae (14h) 
also last term tie &glb)read LAA for £h? 
* 3 Ay 4 
77 6% ne read [yur 8 [BZA ]} for fya= E4224} 
78 Case HT read Uniformly Loaded for 
Leaded &@ 
2 


79 CaselV last equation read Berd, a 
for Fat Ba! 


93 G0 read [i 2tmfor /] Bin 


Sh he 


wig 
us 
Myint 


Westen 


test ctrevert A 
ta) 


.- 


; y ‘ 
Anya 
hanks 
APNE 
are 


he 
Tetbas Price 
mii a ceutt 
via peers te 
a hens wh quate 
} 


Sang Adee - A : oe - 
‘ S : . ~~ : as 
- ¢ ‘ “ee . 


behter 
ant 


yi 


ANE, Uehiro 
i Pon eat 


sod 
het! 

Dircsalenal ts a 
ee 


ahah 
Pane 


at Coney 


Beiter ot 
ison air 
Ar 


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